Primer_diff_enacbe_analiticno_colab.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.0"
    },
    "toc": {
      "base_numbering": 1,
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": true,
      "title_cell": "Kazalo",
      "title_sidebar": "Kazalo",
      "toc_cell": false,
      "toc_position": {},
      "toc_section_display": true,
      "toc_window_display": true
    },
    "colab": {
      "name": "Primer_diff_enacbe_analiticno.ipynb",
      "provenance": []
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pUMPiVRLaAb0",
        "colab_type": "text"
      },
      "source": [
        "# Primeri uporabe simbolnega računa za analitičen izračun prehodnega pojava\n",
        "\n",
        "Prikazali bomo primer uporabe knjižnice Sympy za analitičen izračun diferencialne enačbe prvega reda za nekaj primerov RLC vezij.Pri tem bomo v vsakem primeru pokazali malo drugačen način reševanja ali izrisa rešitve.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RgBhQgf9aAb2",
        "colab_type": "text"
      },
      "source": [
        "***\n",
        "## Vklop zaporedne vezave kondenzatorja in upora na enosmerni napetostni vir \n",
        "Rešujemo diferencialno enačbo $R\\frac{\\text{d}i}{\\text{d}t}+\\frac{i}{C}=0$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qSVSEifSaAb3",
        "colab_type": "text"
      },
      "source": [
        "Vnesemo potrebne knjižnice, pripravimo spremenljivke, tvorimo enačbo in jo rešimo."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jkwubJesaAb4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "outputId": "42ba5990-32c8-4950-bcde-83dc7bf404ad"
      },
      "source": [
        "import numpy as np\n",
        "from sympy import *\n",
        "from IPython.display import *\n",
        "import matplotlib.pyplot as plt\n",
        "#matplotlib inline \n",
        "from IPython.display import Math, HTML\n",
        "\n",
        "def load_mathjax_in_cell_output():  # Te vrstice so potrebne, da se izpišejo enačbe. Potrebno le za Colab \n",
        "  display(HTML(\"<script src='https://www.gstatic.com/external_hosted/\"\n",
        "               \"mathjax/latest/MathJax.js?config=default'></script>\"))\n",
        "get_ipython().events.register('pre_run_cell', load_mathjax_in_cell_output)\n",
        "import sympy\n",
        "sympy.init_printing()\n",
        "init_printing(use_latex=True)\n",
        "\n",
        "var('R C t C1 a Ug') # priprava spremenljivk\n",
        "i = Function(\"i\")(t) # funkcija toka\n",
        "\n",
        "de = Eq(i/C+R*i.diff(t)) # zapis diferencialne enačbe\n",
        "display(de) # izpis enačbe\n",
        "des = dsolve(de,i) # rešitev enačbe\n",
        "display(des) # izpis rešitve\n"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAhCAYAAACr3SvgAAAABHNCSVQICAgIfAhkiAAABvxJREFU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\nFClSpEiRIkWKFClSpDie8B9/JAnfyznlhAAAAABJRU5ErkJggg==\n",
            "text/latex": "$$R \\frac{d}{d t} i{\\left (t \\right )} + \\frac{1}{C} i{\\left (t \\right )} = 0$$",
            "text/plain": [
              "  d          i(t)    \n",
              "R⋅──(i(t)) + ──── = 0\n",
              "  dt          C      "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAaCAYAAACzWm4FAAAABHNCSVQICAgIfAhkiAAABZtJREFU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\nJEjQp/EvEs57NPqeB6wAAAAASUVORK5CYII=\n",
            "text/latex": "$$i{\\left (t \\right )} = e^{\\frac{1}{R} \\left(C_{1} - \\frac{t}{C}\\right)}$$",
            "text/plain": [
              "             t\n",
              "        C₁ - ─\n",
              "             C\n",
              "        ──────\n",
              "          R   \n",
              "i(t) = ℯ      "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NTumMNjvaAb8",
        "colab_type": "text"
      },
      "source": [
        "Rešitev diferencialne enačbe je ustrezna, le iz začetnega pogoja je potrebno še določiti konstanto $C_1$. Ta mora izhajati iz pogoja $u_C(t=0^+)=u_C(t=0^-)$. Torej mora biti napetost na kondezatorju ob preklopu enaka nič. Ker mora biti hkrati zadoščeno 2. Kirchoffovemu zakonu, mora biti napetost generatorja ob preklopu enaka napetosti na uporu $u_g(t=0)=U_g=u_R(t=0)=R i(t=0)$ in torej $i(t=0)=U_g/R$.\n",
        "\n",
        "V tem primeru bomo to upoštevali \"ročno\", tako, da bomo sami preuredili rešitev enačbe, saj lahko člen $e^{C_1} $ zapišemo z novo konstanto $a$, torej lahko tvorimo enačbo $i(t)=a e^{\\frac{-t}{RC}}$. V ta namen bomo uporabili funkcijo $Lambda$. \n",
        "\n",
        "Ker je $i(t=0)= a$, je $a=U_g/R$. S tem smo prišli do končne oblike rešitve."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EfV6F-V0aAb8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "12d40489-591c-49a2-a325-0b9c3a643226"
      },
      "source": [
        "des = des.subs(C1,0) # za C1 vstavimo 0 in nato s funkcijo Lambda spremenimo rešitev v bolj praktično obliko\n",
        "display(des)\n",
        "\n",
        "\n",
        "f = Lambda((t,R,C,a),(a* des.rhs)) # ki je a*(desna stran enačbe - rhs=right hand side)\n",
        "a=Ug/R # a je očitno tok ob času t=0, ki je enak Ug/R\n",
        "display(Latex('$i(t) = ' + str(latex(f(t,R,C,a))) + '$')) # izpišemo rešitev z uporabo Latex sintakse"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAAAYCAYAAADwF3MkAAAABHNCSVQICAgIfAhkiAAABH9JREFU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\nHXXU0VH4G7t5GRb1l++VAAAAAElFTkSuQmCC\n",
            "text/latex": "$$i{\\left (t \\right )} = e^{- \\frac{t}{C R}}$$",
            "text/plain": [
              "        -t \n",
              "        ───\n",
              "        C⋅R\n",
              "i(t) = ℯ   "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$i(t) = \\frac{Ug}{R} e^{- \\frac{t}{C R}}$",
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lHR_Nt9OaAb_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "e8d326b7-b0b6-43c7-c19f-078fed474831"
      },
      "source": [
        "#Pripravimo za iziris\n",
        "x = np.linspace(0,15,100)  # niz vrednosti za x-os - čas\n",
        "plt.grid(True)\n",
        "plt.xlabel('Čas  /s',fontsize=12)\n",
        "plt.ylabel('Tok  / A',fontsize=16)\n",
        "plt.plot(x,[f(t,1,4,1) for t in x],color='#008000') # ob izrisu vstavimo vrednosti za R, C in a (1,4,1)\n",
        "plt.show()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEKCAYAAAD5MJl4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oTQU0V1xaAcB",
        "colab_type": "text"
      },
      "source": [
        "## Vklop tuljave\n",
        "\n",
        "Rešujemo enačbo ${{U}_{g}}={{u}_{R}}(t)+{{u}_{L}}(t)=iR+L\\frac{\\text{d}i}{\\text{d}t}$.\n",
        "V tem primeru bomo preuredili rešitev tako, da bo možno neposredno uporabiti začetni pogoj, ki je $i(t=0)=0$.\n",
        "\n",
        "Najprej zapišemo enačbo v obliki $ L \\frac{\\text{d}i}{\\text{d}t} ={{U}_{g}}-i R$ in nato poiščemo njeno rešitev.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ij9JP_IIaAcC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        },
        "outputId": "aee8db8d-047a-4f62-e53c-dfcf5482f680"
      },
      "source": [
        "i = Function(\"i\") # pripravimo funkcijo in spremenljivke ter zapišemo dif enačbo\n",
        "L, R, Ug, t, i0, C1 = symbols('L, R, U_g, t, i0 C1')\n",
        "eq = Eq(L*i(t).diff(t,1),  Ug-R*i(t))\n",
        "display(eq)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMcAAAAhCAYAAABtGL9ZAAAABHNCSVQICAgIfAhkiAAABo9JREFU\neJztnHuIVUUYwH+7meuyQfZATDDKbNu1h+trTTIpUotckh4GFblrRFgoZAQ9IFJMMI0Sos0KS0Xs\npT0owtbQTJPNTLcstzLrRg9rs5clm6m7/fHNtGfnnsecc7177907P7icZeb7ZuZ8c+bxfWfOgsPh\n6HFmAnty3QiHIymlWSy7BmjJYvkOR1bJ9uDYmcXyHY6CoAbYCLQDu4Ba4CBwZS4b5XDkmrOBP4GF\nwFBgCpACOoFBFvp3KdkbjfQVQBtQEaMto1RZt8bQKTacvTNgA3LDEyzl3wZWG2nPAD9b6q9W9VV6\n0sYAHUhH+jEH/w4GeBXYB5xgWX+h0oTYwPtrA7YA00L0epu9y4B/kZ3KcSFyu5B7qE5aUQnwB3AU\nu5sdrCocY6Q3IoPGhtOBKlW3pkm1ozxAZ5Wq9xyfvFqVd79l/YXKr8gDPQ+YCzwErAGOIPc/J0Cv\nt9lb1785RKYCscsBMvCzK1VFuy3lr1KV9jXSm4GHM2hDB/B0iEwr8BfdO9jM/5bsBhxyyRCknz73\nyZup8lKWZeXa3g1Iey9JoAtwh9J/NETmYiWzMU7B5s2MUtePLPU7kaWszGjIWOwiVZeqMhZ70m5B\nOuFFH/mFSr4KWdk66NpS3OyRewGZISfZ3EQBMlpd/fppnboO8MnrjfbWtvgwREbvbLbHKbhPQEW2\nhWwHDgGPAIsQIzaqPJt3HCPVdYcnbSKyrWv2kd+BOI71wFZgvSfvXc/f76vrJOy3d4VE2OAYqq6t\nPnm90d56QrcZHGEyaWQ6OPYBM5AZZjqyWiwH7ga+tNA3O6sCCQu3Ig6WyUtAf6SzVhC8FdBGiAoq\n3KnKs6UFeC2GfLYI6qdTkYkKpE9Mcm3vY005MAz4HfgqRC7R4PBSgjgsR4gXzssEcy+rfZ6mEJ2l\nSmZ0iAzIO5efImRSpEd8wn7LI8rrCXTQpBMZCHOB+cBKlX4AuD1AN9f29qOB5D7HOKLbf7KS2Z+g\n/P+pUoV8mkkhMahAlnNvlEHfrN/+V7MNCd2VhcgA/IAM9FyTIt4AXBVRXiXBun8DVwTo5YO9UwHt\nTjoZzVZyC0JkJiuZdSEyvni3VXG3VJkyHAkIePe/7eraL0CnD3A+Ek07FFF+uae8XLIX+CeG/I8R\n+bqfnkOcaZDZsR6J2DwPnImsIl7ywd5LSN/G1gBTkW1bysiL8lv9fCiTC9V1W0RZafgNjqhIVWfc\nSgz0kq5vzBvValPXUwJ0hyEdGWYMkIegP/BNhFxP+ByXxZSPwm8S+w14DFkJpiGRpMcNvXyw9xKf\ntAZkcCynu5Nvw7nq+nWIjD7C9I5P3ihkQqlFJrHbgE1IYKFbWzYjD/64mA1MyrOqvgs8aSVIh/0S\noDNd6cyOKLtaya2NkEtReD7He0hbxvrk6S3EVp+8fLC3Hw0k9zl2Kt3LA/IvUvl7SX9tUYX4Z4uQ\n9tcB3yn5bhNmKbJfPULwW1Ib4nzD0YIsw2bEbI1q4NA0ja5jDPURZc9QcrMs21IolCIO9WH8t0LH\nI5GbDtLPteWrvRtIPjh0sGA96fYYh7yY7ASu8dFtIn0wr8SztdOGqkYctoOkL8ea/cC9EY01v+FY\njMxU5sguQ5bsFtKduLXAtUrHDM/pLd8C4DzV3s+Alw25yYjz+XpEewsN/TLuY/z9mMPAW8gZqKuB\nJ1R6b7X3fOSg60RkddiMBA8qkZW1A7gHeMXQG4xsnWqM9EOIbbuhl8+wn42330z3Mzab1A2Y6NOc\nS33y+iKHFj8IqGMW8AXycPhFKk5EZsh8eB9xrNH9tCxE5jols8GTls/2biCz4yMDEF9mDzIw2tXf\ny+jys0ymIhOJeRxmC3JWLWPCvuHoqxrqHVy257UA7lM6IxK0S4f3xifQLVaKzd51yKrifZ+nJxC/\nLVgsor7hKPVUVgsMBE6KUX4/ZL/4Rsx2lSOh0DUx9YqdYrP3QGRSbwTOQt4NtSLP65BMC7f5hqMO\niQYEneSMYgLwIPHe1lcjb4zPSFhnMVNs9r4emdAPAm8ivklbmIINtt9wPED4GXuHI18oQZ7dRm+i\nGdazYQQSmTC9+pGIA65x/2DBka+MR7ZWO5AXoHOQ53WGVyjJxymd2H3DMRz4JEH5Dke2GYh8jLcb\nCfMeRXzkqKM7kZyGhPWeQpyZKXS9bKnyyKWQU6ODiHdEw+EoaG5ABkQ7clRhHuLYeFeim4DvkZDZ\nkz3dQIfD4XA4HA6Hw+FwOBwORwHyH+OXKs2lgJo6AAAAAElFTkSuQmCC\n",
            "text/latex": "$$L \\frac{d}{d t} i{\\left (t \\right )} = - R i{\\left (t \\right )} + U_{g}$$",
            "text/plain": [
              "  d                       \n",
              "L⋅──(i(t)) = -R⋅i(t) + U_g\n",
              "  dt                      "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dq_VtxnPaAcE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "outputId": "74a9be68-6bd4-4640-bee9-f4713c6dfc22"
      },
      "source": [
        "dsol = dsolve(eq, i(t))  # rešimo diff enačbo\n",
        "display(dsol)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAAeCAYAAADegqmLAAAABHNCSVQICAgIfAhkiAAACYVJREFU\neJztnH+UVVUVxz8zIMwwhT9DrLQURSENBEFJwDGRqAXLX0BiGU8LV/ljpZaVtiwrf2CjBVaGtUxF\nBRWLWtUaYNTIsB9mgJFOReloWaYoRhIoxOuP7zm8886c++O9edcHs+5nrbfue+fse+6+756zz977\nnPcgJycnp040AHvUW4ndiL2BfwFD6q1ISpYAn6pBO/1q0EZOAl8E3lxvJXYRHgSK5rUNWA/M8WTa\ngNsizh8J3A38HdgKPI0Gw5gslA3QBiz3yo4CXgb2DMgvAOY5nx8EFka0PRY4sacK5kRTAD5abyV2\nITYClwODgXcAXwF2AEeb+gFGZnzg3AKwHfgecDxwEDARuAu4NUulHX6OdPZ5DLjAK2sA/gG0OmUb\ngU/GtD8fOLQH+vWYS5GlPMsrvwN4AWipoK3Rpq2P1Ua1HjEYWIkeSo7cziKlgQfwdlP2YfN5Oppl\n/O9sHBqIl0S0vU/t1AzSD3id0qxeBJ506r8ArPLOGQu8BPQ1n+39hwyNZRDQXgN9q2YRUnKoUzYG\nWcxLI865hPAABlgK/BN4Uw11rIYFwIURdf3Rw90M9IlpYx26z2G1Va0uzAT+DTSazwcA9wD/A4ab\nsvlAR+DcXwKPZK1gDI2UDP1YZGj3duqnoOfZ7JRdS7lLOhPda1K/XAKcnEKn/U173/DKV1BuNIpo\nUlsFzEhq9CDgCMqt4QrgFcpvzuUuc5HDA3VjTd0VSRfOkEHAJmC/iHqr4y9i2mhBs8EmSh14d+Z6\n1HleBf6L7v814GJH5ofII3I5zMiemeIaS5EreH9PlQ0wFT2LkKfzbqSjm3R6Ajjd+Xw90JnyOo+m\nkDvPXNOPM19CE9mXgKuAq9H3sd3IR3kXQYaaxr4TI9MJ/IdoF7ATeIb6deKLgN/E1J+PvpivxchM\nMDI/q6FeLgXTfmtG7ft0ALegmGgUsAz4piez3Mi4fBDpmSaWagWmET8Yr6b7zOG/WgPnXUm08bQG\n40jz+VBgC+UhVgeaRJIYgIzWiAS5dmAD5Z7VIUaPPwbkP27qumyBPzhONAJtTtm5aJDdG2hwrpE/\nAk33Oyh9gWc7cvegGTfNdJ8FpwKPx9QfY46/jZGxGcLHaqJRNpxBqVO8jrKjVxB2vUchd/MvwGrU\nOc5H2UjLBsrdP1DnBM2oSaxERjqOecjtj3uFZqaRwJqINm3M+qI5nooyp5sdmVHA7xJ0A3kN64HT\nYmQGAu8FfowGrsX2q9B1lpnjIFvQ1xMYZY6rnbJJ5gK/DjS4Grkxs9GDdeOLlc57G1+cTPdUdNb0\nBY4Dvh8jM9oc0wzGOJl60QdZ+TPR4FqCXM73A9eg8GG2I38w6rDrnLIu1LnPBj5jytagGdvlD+Z4\nAmEDPQB14LRsMK9KGUF0cuVI4Dm0PgpwCuXutr3/1aRjDcoURzEVJZWWeuVxg9F6Fjtd5aTB2IIs\nUCflVsVyH7AXetB3EO3K2g4cd0OgeGWvBBmXtSiuiWMI6iDPRNQ3o4TFRtSRo9iVB+N8NBDnIvdt\nuym/DBnFj6AYyWYcRyMv5knK6UBxlR2My815+6LYB3T/7ShR0YwMbRH1nTkoNvIzmVnQF3lkb0WD\n/xWnbgIlo/8WZIynO/XW+G6j5MqCJp1QHPkscFKMLqeh8bHCK7eD0fem9gNuMO/nRjXqx35D0Rft\nX8RlgZE5JkYG5LM/nyDTRXL84L5uT2gPYLKRjTIE40i+x32MTDUWPC0FqosZj0UDK8oo2cTCOU7Z\ndcCfA7InGdl3OWW/ovuaXX80YH+POuFGZP2/DDR5sq1kk8D5ENpssAP4tlPehLLEx5nP5yKvzeU6\nwv1pHWE+b+oHBOqa0JhZ4pU3IANRRAPvKrQmutCUbwI+EXVzLcgyuEGx7aghd8TyKIpP+sfIgNyG\n7QkyWTAT3cPIiPqLTP01MW3YAb0sRqYSuqid0bGZ7EXogfuv+019tZsdpgB/In7JJ45WshmMUVxA\nuWH9EaWZvlpsHzkgUDeN8LKenchCr1fR91qG66aOQAkd14/eYo6+tXPPPwq5O69F3opodtp7I7FG\nIuraoTjZx1rZNCnuNMyjuzs+klJs0+XVrY1pa7I5zkq4ZpSbnsQy4FtoQ0ClbTyA+lULmsVmoJk2\nS7ahwWN5BFjcwzZtDByacE5Hk9FPvXLrKd6GZmeQhzUbZe0Xo9h1p3vtDkbbKd0M1QvmuG+EksPR\nQE0KhBtR53s6QS6LmHGrOUbtHLIu2VMxbXzAHB9IqVcS8wJlBTQYb6c8+RVHE4qJHkYJlay4qcrz\nJtVUi3T4eYuv1qBNuzHAN+h90Mz4EHKNXULx4svA15HHOQMly/xNAoD2GBbRgqmlAQ3IF0MnoMRA\nkXJLFGKYkYvLaEI2MeMkIxvVWdeY+vdF1B9v6v9K96Wg0Wh/5BaUZXwPssytKfTyKVB5zNhsznmi\niuvlpOdKFJv6M6NdCjwvcM7Dpu7YQJ0Ne/xYdidrUafyM6w25ggt8tptcLMDdS7nGLmo7WhZYvcg\nTouotwmoDrq74+OQa1akfPcGKJO3CVneYSi9/TcjW8nsbilQXQLn8Qj9LOOpPt7LEW3Izfa5CeVZ\n9vfKG1FSZxvhEG8PlPTagbLBZdi9maGYaBZ62H5GDZShLBpF21DCILTfbjFK3hwYqMuaRuRCXBxR\n/zZKg+g5tEFhIVpXLaIvO5QAWEH3mX4h3eO9tBSobjBORg/dGpQbkSt0H5rNn61Sn5wSP0AL+i4N\n6LsNLeMMR88jLta/m4hxZTfdLgic1A8tnkZtJ7sQZdu2Es5K7olm3KTYLkvaiXdpB6E4bj0ySlvM\n+1spxdIuB6J79bdIfRdl76qhQPXb4cYgD+Z5NDA3oDT9LcSvj+Wk4yng017ZGPS8Qj+esOFb3E/J\nphuZhypV5nJz4tFJggFsWjjupypZM4d4K1Upp6BO7+/FXYUWvXN6DwORO3mwV34t6td+eeY0odjJ\nn6qTaEY/6Hwj15lCDERJqFq5yVPRA3IztNa7iIrdcnZPzkL7Wn06qa2Br4iJ6C8rKvlx8TAUR74z\nA30q5TLgczVqazByZW9GCaIp6OEU0U79nN5DO/X7gUOvpRn9/KlWf0Y1EyVrNgM/AT5LaV02p3cw\nhPrmOno1E4j+t4Ke0IA2Jt+cQds59eNOAksPObVjFt1/o1cp41E27BCUVVuEMs75g+s9TEQbPnIy\npqd/SjUdreFtRWuUd6K9mzm9h/yPy3JycnJycnJycnJycnJ2Gf4P4zhmgdFmdicAAAAASUVORK5C\nYII=\n",
            "text/latex": "$$i{\\left (t \\right )} = \\frac{1}{R} \\left(U_{g} + e^{\\frac{R}{L} \\left(C_{1} - t\\right)}\\right)$$",
            "text/plain": [
              "              R⋅(C₁ - t)\n",
              "              ──────────\n",
              "                  L     \n",
              "       U_g + ℯ          \n",
              "i(t) = ─────────────────\n",
              "               R        "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y_0Cj-FdaAcG",
        "colab_type": "text"
      },
      "source": [
        "Sedaj se želimo \"znebiti\" konstante $C_1$ in izraziti enačbo z začetnim pogojem, t.j. $i(t=0^+)=0$.\n",
        "\n",
        "To naredimo tako, da izrazimo enačbo za čas $t=0$ in jo rešimo za $C_1$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T4m32wN0aAcH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "outputId": "3179cb69-5077-41e0-a2d0-6f8610caec83"
      },
      "source": [
        "it0=dsol.subs({'t':0})\n",
        "display(it0)\n",
        "\n",
        "init_solve=solve(it0, C1) # rešimo enačbo za C1\n",
        "\n",
        "display(init_solve)  # prikažemo rešitev"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAAAdCAYAAADxYhOxAAAABHNCSVQICAgIfAhkiAAACJJJREFU\neJztm3uUVVUdxz/DEDJOZdKL4tEgj8QsyWkkw2gsRVeRLA1Iy2xqpbUsVkSlC9dqVasi0iR7Idby\nAQY+smWtcmGMkhFibylRMlLHLFECcUwgQJn++O7d2Xffvc89c8+93Jk437XuOnd+e+/f+d1zfr/9\ne+2BAgUKFIigudECDCBMAVYC/wD+AzwC/BDoyLj+TqDPfPYDW4DzA/OWAVd461ZEeBbvpwEYAnyq\n0UIMEHQBzwHXANOAscB04AfA1Rl57AQWAiOB1wBfAg4Ab3TmNAGPA53euk9GeL4dGWxDsQBZ+/s8\n+nJgG9Cak3+74f+RnHxqhcXA6xotxADAicgoYpvEiAw8xqN36xrBaEM716GdAOwAhnrrTkrhvQx4\ndQYZ6oZVSMhJDq0DWf2CyJrRaJd5HNgL9CA3eWRk/q3AVuCF+cXNhWmUunOLw4B9wC7S3fh96FlN\nrr1oBx0bgLtz8pgL9CIvDPAq4EbgeeAYZ94iSsOmuWZOmj60ATdnlOOVht+3PfoakjDPfrYB64E5\nlZiOBY5G7s5l+DTQEpg/HnjS3OTHaAdea/7+C/DSwJoTzPgllYSpM9YBxwboVr5fpaxtRTvsMySK\nMFgxEf3eszPMvRWFPbcExr6GFPJZYLfhuReY7827HzjLW7c5w71XA1MzzLvA3Ptkj74DbfBfBL4A\nfBn9jufM/H6F1JMMs+9Fxn9umM7z6EsMfVlk3WbgURqnVKcBf4iMXYhkX5Ky/q1mzi9qLJdFl+Hf\nWSf+Lt5r7jUhw9xO4N2EDaMbuMrwOR64HfiON2cCsIfSkLwb5TGVcDZwR4Z5q4HtlHr7o0g2ax8f\nM2M9MYYnmwmXObTFhvaOwHwbGz5CuYK/CO0cuwjnJZ83a0+LCVNn3ARcHhm7Bsl2Tsp6m4tdljIn\nD7qojWG8h0RR9qEq0SWUKs2HzL1GZuTZSdgwdgAfdP5uQ5vq6x3aZ4CfBdZl2a1HGn5tKXNejLzU\ntR59LvqNKwNr2szYbkvwlfl4c/2jQzsFucdfBxhaV7XGCOzi3yhmPRx4c2CtjWdPDYzVG83A6cC9\nkfF2c/1dCo+ODHMaiWbgBqTAE1DJdSl6T19Bxm+xyVzfFuF1eIb7jUMJ+n0OrQc94w84tFko5PbX\nuToXwxMobH9XypyZwDAU8rl4k7mGogTrKf8Xzg31JviG0YrKZJvRzu/jteb614iQW4AZKBy70xuz\nCjU9stZiPvCSCnNcbKT0wYdwLNpZ/hwYa0GJ4k7gbyk8BrphfBOFHouBz6E4GuCzwF3AeSi2fwD9\nhtUoWW1Bm1Yf0ofzUUy+vsL92pHRPeDRu1E+cRHwcrRJzvbWgXoebr73POG8YyMqmnw3IseZSFfX\neHRrGL/36C8Dvm6+L7bEkGE8S6Loo9DOszUixBHm2hsZt/SQYveiBtLYyFqL+agenhXLqWwY1qD/\nFRibgp6L/wBdjEBh5A4URg40TEV50k9QT8HFfvSM3mLmWUU+E/URFiCl2wc8DNxG+rOwaAceQu/U\nRTdwMSqJT0VG+KS3DsorYpsoDcEstlNa4XIxHEUCqz05mkg2/TNQX6QZ6dUZKHK6EHlVoNQwWtHO\nvgHtFpBUlHZGBMmLp1BpLQ1tdbjvKHN9JjBmd5Y0TxDbfapFD3HjDyX3y1EOEsM8pAy7UfXFh92Z\n3VB6L3Cp+VSDhZQbIShSsBXORZRvWrF1MfSSvD8fp6KSrx9GTSTZxD/tje1CHux2l+gaxnHoQbmx\n3h5zHZ4iJM5NfVj605HxFuceBxOtyFWHwsNQnuXD5ky/rZE8V1DuVaegeHw55dWSjRX4zTDXtOIB\nqCrYX9yBdKUVHRuZA9yTce3dKO/Jg17iTeazkKe7zaPbjexa4MPm+whUKFhiZBqHo6euYViFcBPS\nbeYa6kUAPGiukyLjE801lIMMQcpQKRSpR45xwNy/icQ7Wtgu+MMp699prllKh1kQajJ2IcO4DuUE\nWTEcxfLriCfTeXBKjrXVeiMXQ9Gm5qMZlZHXUh7ahzz8U8A3UMd/DioQ+A1BIClRvsGhNSHjCMXi\nkK9cO9ms/VGEt0UP5d3KtM91FfiBQo0+lID7uJf0MvI0M/4Q4R5MO/BL5Ak3oVh+P/0vu3ZRXbm2\nxay7v5/rBguuBB4L0G2r4YLA2DozFmoOzjBjG2I33Ihepp+Q30J686faBp+tnX8iJlAdMcvce3Rg\nbJkZ66Y8hDwRhR99lHZuLY5GeculyPBnopfYR/+8HuTrY/wpRUbQmaTBemJ1FeEK2beQJ/Fz1iGo\ndbCfcErwApRDHyBwFsueDQrFzOegh/zxiKD+kZCvkhwJeZB4GHYDKiGOiYzXExOI7yCjSJT5n+is\nzwrUx+lDD/+iCN81lHvAFaR0VFPQRfWGMQMpgjXwy1HYcDPydH+vgudAwV2ou+6iCf2mkMEcg55D\nWl62koiO2xOvod19GFL836QwHoMSm63IwB4l/RDhEcg7VcoF6omtwEcjY69A8m9Bv2eP+X41SS7m\nYwx6hsd59O+jsml/0UW+zncH8vZPICPZjppvVxE+xTAY0IQS5Pd79A70rEKHXM8zY2nH5mebOWv7\nK9BCyo8T54GN8dOOGdcbV1K+8+TBLKSATR59PWqQFciP8ag/4Yeli5A+jTvYAg1HXuCnNeDVgo6n\nh87aHExMQZUnX5GrxUwUp7qFBuuJY7F+gf5hHuVnoEAd8kol7LphOjr4l/cflSajplNbTj61wCrU\nBa0FRqKQayna2U5HL6wPnewskB/3UPmkRIEaYBzh05bVYi5KtHehE6QXk/SCCuTDNOKnoQvUAeeS\nNOxqiSZUyl5aB96HGoahfPCwRgtyqKHivzVmwEmounEUqpKsQtW8hv6f8v8JOlE3v8AgxGyS06WP\nAdcTbiAWKFCgQIECBQoUKFCgQIFDDP8Fw/ALuQ6I+kQAAAAASUVORK5CYII=\n",
            "text/latex": "$$i{\\left (0 \\right )} = \\frac{1}{R} \\left(U_{g} + e^{\\frac{C_{1} R}{L}}\\right)$$",
            "text/plain": [
              "              C₁⋅R\n",
              "              ────\n",
              "               L  \n",
              "       U_g + ℯ    \n",
              "i(0) = ───────────\n",
              "            R     "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALoAAAAaCAYAAAAAEkYfAAAABHNCSVQICAgIfAhkiAAACEdJREFU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\nHDlypMA3X5c/K7XEj2cAAAAASUVORK5CYII=\n",
            "text/latex": "$$\\left [ \\frac{L}{R} \\log{\\left (R i{\\left (0 \\right )} - U_{g} \\right )}\\right ]$$",
            "text/plain": [
              "⎡L⋅log(R⋅i(0) - U_g)⎤\n",
              "⎢───────────────────⎥\n",
              "⎣         R         ⎦"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YJnltAQxaAcJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "457daa68-9f3a-4e0d-a126-6df7e2bbc853"
      },
      "source": [
        "final = dsol.subs(C1, init_solve[0]) # v rešitev vstavimo C1 in dobimo končno enačbo\n",
        "final"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUwAAAAeCAYAAABHXycXAAAABHNCSVQICAgIfAhkiAAADKRJREFU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\nQmCC\n",
            "text/latex": "$$i{\\left (t \\right )} = \\frac{1}{R} \\left(U_{g} + e^{\\frac{R}{L} \\left(\\frac{L}{R} \\log{\\left (R i{\\left (0 \\right )} - U_{g} \\right )} - t\\right)}\\right)$$",
            "text/plain": [
              "                ⎛L⋅log(R⋅i(0) - U_g)    ⎞\n",
              "              R⋅⎜─────────────────── - t⎟\n",
              "                ⎝         R             ⎠\n",
              "              ───────────────────────────\n",
              "                           L             \n",
              "       U_g + ℯ                           \n",
              "i(t) = ──────────────────────────────────\n",
              "                       R                 "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l_aDVobvaAcL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        },
        "outputId": "58935f99-6f9d-4488-e182-841dbb19a96c"
      },
      "source": [
        "expand(final)  # drugačen izpis"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU0AAAAdCAYAAAAuCT6HAAAABHNCSVQICAgIfAhkiAAACUBJREFU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\n",
            "text/latex": "$$i{\\left (t \\right )} = i{\\left (0 \\right )} e^{- \\frac{R t}{L}} + \\frac{U_{g}}{R} - \\frac{U_{g}}{R} e^{- \\frac{R t}{L}}$$",
            "text/plain": [
              "                                -R⋅t \n",
              "             -R⋅t               ─────\n",
              "             ─────                L  \n",
              "               L     U_g   U_g⋅ℯ     \n",
              "i(t) = i(0)⋅ℯ      + ─── - ──────────\n",
              "                      R        R     "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MxFcQslfaAcQ",
        "colab_type": "text"
      },
      "source": [
        "Vstavimo začetni pogoj $i(t=0^+)=i_0=0$ in dobimo končno obliko:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X-lbpvIEaAcR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        },
        "outputId": "cc4f9d95-8d73-4048-ef4d-577371970183"
      },
      "source": [
        "zacetni_pogoji = {i(0): 0}\n",
        "i2=final.subs(zacetni_pogoji)\n",
        "simplify(i2)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN0AAAAdCAYAAAAuLGmuAAAABHNCSVQICAgIfAhkiAAAB4lJREFU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\nRU5ErkJggg==\n",
            "text/latex": "$$i{\\left (t \\right )} = \\frac{U_{g}}{R} - \\frac{U_{g}}{R} e^{- \\frac{R t}{L}}$$",
            "text/plain": [
              "                  -R⋅t \n",
              "                  ─────\n",
              "                    L  \n",
              "       U_g   U_g⋅ℯ     \n",
              "i(t) = ─── - ──────────\n",
              "        R        R     "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zmKaJT89aAcT",
        "colab_type": "text"
      },
      "source": [
        "Poiščemo še rešitev za napetost z odvajanjem toka (desne strani enačbe i2) in množenjem z induktivnostjo L."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eJ1_SqzkaAcU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        },
        "outputId": "0e1ab950-fcba-461b-b018-42ed1637a414"
      },
      "source": [
        "u2=symbols('u2')\n",
        "u2=L*i2.rhs.diff(t) # množenje z L in odvodom desne strani enačbe\n",
        "expand(u2)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAE4AAAAdCAYAAAAEsFpEAAAABHNCSVQICAgIfAhkiAAAA6hJREFU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\nJvZgv4o94LPiz5E2bdq0aXMA8xeh5OKcokx//gAAAABJRU5ErkJggg==\n",
            "text/latex": "$$U_{g} e^{- \\frac{R t}{L}}$$",
            "text/plain": [
              "     -R⋅t \n",
              "     ─────\n",
              "       L  \n",
              "U_g⋅ℯ     "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tDIR0uLdaAcW",
        "colab_type": "text"
      },
      "source": [
        "### Pripravimo enačbe za izračune\n",
        "\n",
        "Pripravimo podatke in uporabimo funkcijo \"lambdify\" za pretvorbo iz simbolnega zapisa v numeričnega."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NifqUA9SaAcW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "outputId": "e96b0642-c86b-4658-c733-407775a16dd6"
      },
      "source": [
        "podatki = {L: 1e-3, R: 5, Ug:3} \n",
        "tau=L/R  # časovna konstanta\n",
        "tau2=tau.subs(podatki)  # numeričen izračun časovne konstante z zamenjavo oz. vstavitvijo vrednosti za L in R\n",
        "print('Tau = ',tau2,' s')\n",
        "print(podatki)\n",
        "tok = lambdify(t, i2.args[1].subs(podatki), 'numpy') # tok kot funkcija časa\n",
        "napetost = lambdify(t,u2.subs(podatki), 'numpy')  # napetost kot funkcija časa\n",
        "\n",
        "\n",
        "print('Tok pri 0s: {:g} A'.format(tok(0)))\n",
        "print('Napetost pri 0s: {:g} V'.format(napetost(0)))\n"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Tau =  0.000200000000000000  s\n",
            "{L: 0.001, R: 5, U_g: 3}\n",
            "Tok pri 0s: 0 A\n",
            "Napetost pri 0s: 3 V\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3OV9yfP1aAcY",
        "colab_type": "text"
      },
      "source": [
        "Sledi priprava enačb za izrise. Naredimo dva niza: cas za izpis gladke krivulje z več točkami in cas2 za izris simbolov v redkih točkah:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "no89PIKkaAcZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17
        },
        "outputId": "63c97061-4d90-4ce4-dbcc-fc2ca94a48eb"
      },
      "source": [
        "cas = np.linspace(0, 1e-3, 100)\n",
        "cas2 = np.linspace(0, 1e-3, 5)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B8Sb175LaAcb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17
        },
        "outputId": "10c6fb79-5ce3-449c-d6cc-6f5e9a1deb86"
      },
      "source": [
        "def slika():\n",
        "    plt.plot(cas, tok(cas), 'C0', label='Tok [A]')\n",
        "    plt.plot(cas, napetost(cas), 'C1', label='Napetost [V]')\n",
        "    plt.plot(cas2, tok(cas2), 'C0o', label='Tok - velik korak')\n",
        "    plt.plot(cas2, napetost(cas2), 'C1o', label='Napetost - velik korak')\n",
        "    plt.xlabel('Čas [s]')\n",
        "    plt.ylabel('Tok [A] / Napetost [V]')\n",
        "    plt.legend(loc=(1.01, 0));\n",
        "    plt.show()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1rB8x_B3aAcd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "3184ad78-1a4e-44a5-dead-af1b15d2f2bc"
      },
      "source": [
        "slika()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAEICAYAAAADc72lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UbNcA-FZaAcf",
        "colab_type": "text"
      },
      "source": [
        "## <font color='blue'>Vklop kondenzatorja na izmenični vir napetosti</font>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ung_oQy6aAcf",
        "colab_type": "text"
      },
      "source": [
        "Rešujemo enačbo ${{u}_{g}}=RC\\frac{\\text{d}{{u}_{C}}}{\\text{d}t}+{{u}_{C}}$, \n",
        "kjer je ${{u}_{g}}(t)={{U}_{g}}\\sin {(\\omega t})$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2aDLEawBaAcg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        },
        "outputId": "eeac6bb1-8e39-4d22-e7fd-00413b1cc42f"
      },
      "source": [
        "u = Function('u') # pripravimo funkcijo in spremenljivke ter zapišemo dif enačbo\n",
        "C, R, t, Ug, omega, u0 = symbols('C, R, t, U_g, omega, u0')\n",
        "eq = Eq(R*C*u(t).diff(t),  Ug*sin(omega*t)-u(t))\n",
        "eq"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQQAAAAhCAYAAAA/HtU7AAAABHNCSVQICAgIfAhkiAAACVVJREFU\neJztnHuwVVUdxz8XeV2xJCUeNubJxMBKBeSqhUxOmaU3eyFFb5sGybIRKhptmnDMQa+pZRNJjmEU\n0RhljT3RQHyNmRcppquNQZcKRRJCGgTBOP3xXWvOvuuuvfZ57HPuvrA+M2f2vWv99trr7N9v/9Zv\n/dY6GyKRSGQQMA94aqA7EYkcTgwZ6A4EOB3YMNCdiEQOJ4ruEB4f6E5EIpHWczqwFtgLbAQ6gD3A\nBQPZqUgk0nomAs8D1wEnARcCvUAZOK6J1/0+sB0YVcM501C/PtWUHg0eSug+3JFzu/XopFEGu05b\nZscTgcVAN/Bv4IA53gtcBhyZkF1tLpD8bAceBC7OuM7vgB85ZbcBz9bS2RqZDhwEFqTUz0ff4UOe\nuruAZ4CjmtO1TEYA+1EEdURAbiP6DpOb0IcS+TuELJ00SpF1Wi8tseM24BpkdGXgIeA7aARfCeww\n5Q8kztlhOnY1sAj4GrAKeMnIzk+51vGmfrpTvgQ5imaxGtgFtKfU/9D063Weug5Td1VzupaJvf4D\nAZlR6N7vpjl5omHAJGBCjm1m6aRRiqzTemmJHS8zgn8BTvPUtwNfNnIAJxr5Jz2y80xdb8q1LkKG\nO9wpfwS4PqujdXIycl7fDcg8AfwXOce0+i0MTFL2MnRPbwrInGNk1rakR41TjU4apcg6rYeW2PEC\nZEg9wMsyOmS90mxzzgqPTMnUvZDSxrtMffJa1pg/mHF9gCuN7Ps8da82dXc55deZ8rd6zrF1vs9H\nE3JfNWXnV9HHvPmeufacgIzV4w11tH8R8HsUTr4IPA2sQ47IUsI/ZUiWl4AfA88B+4DHgM6Ua4Z0\nAnCpqb8xo++bjNw4T9tF1mlh7HhoonICcC0asWcjzxJirzmeYY7dHpmTzPGJlDYeQ0b3daALhaFL\nTF01exCmJdpxsdOQ9U7524D/oSjEZT1K0nwceBi4J1F3X+Lvh8zxPJo7tfFhv/MfAzLTq5DxMRdY\nCmwD7kYP81jgVOASKrrJ4gTgUWAz8APgGOADwC/Q/Xcjl5BOxiHb2IYMOEQ3iljfROUBGkw6LZQd\nX4+8xTK3IoM15ryZTvkY9FCXCScW56CwZS/q/NUoYVZN6PZ3lOj0sdhcOzkq2bn1xkCbc815cwMy\nRxuZRzP6dwXKqVT7eU9Ge+0oubszQ+5vpn+vyZBz6UYOeqynbkzi7xLhCKFM/4f3fFP+a6c8Syff\nNuddHuq4ocvIXumU56nTZlBIO/6rqTw30IBLG0pqlNEovwglJJeb8t3Ap2torxaOMdf9bUr9PfRf\nujzZlK0OtHurkTkjIANyYNsyZHpJD918nzsy2jub7P7b+/JcRls+upEzfkWGXImwQ+jFvwKyxdOv\nkE7GoOnG8/Rd1UrDhsBdTnmeOs2bQtmxnTIclbjIHzIaSDIReRmAzzt1e4BZpH/RRplqjr4wCxSG\nbUdzYMux5vifjHYPEPa+oFF6XIZMKaO+VqxyQ1MBK5N2X0KsQPP0HjT/X4fCyrTRK40NKJx1+Sdy\naklCOpmNllnvpG8eqgPlSW5BUaXFOo0XnXby1CnI4Z1QhZxlBfCRlLpC2bENy19pjrtJTwD6sMa3\nDEULbaazC1BYsxIYXUN7tWDnXb7cxYlolHPnXTbvMTKlzaHAG9ED4RqVS3uivVZhjcf9XknOMsd6\nQt+b0LxzC/A5NA9/Fs35s0aaJLtSyl+i/1QwpJO3mOM6p7wT5SRcHdmcVfJHcc3Q6SYUUVf7edrf\nDFAwO7YRwp5E5RH4vbsP32i0E7gZjQQXo6zmtxL15SrbDtEGTDF/+x4Ou+XZ/S3EdnM8Fj+noJsc\neuBARj0azf1CXEFtDnED8PNA/evNcXNAxn73ez1109BD34GMei562M6jkmxabj6jUXLuvcAnUdJp\nErVHC1mEdGLXz90lbZsV/0eibAgww/yddCB56xTSV0PqobB23Et46SfZiOV+c86ZHrm3m7qHPXV5\nsAFtnnIZQWWX3iynrg3dzDSj/hjVJbAmG7mfZsj1km8O4XHCS2NvNvWb6D8ST0IRYJfpfycK4ctk\nO63bjdz7zf+llP6mlVvuo/+AENJJr5FP7oex974MvDxRbu3NzbrnrdO8KZQdJ43mZnNcgozHpQ14\nJ5pb2nOnoDDwTx75tSh0PIvqf5NQyzsQ9qMdcxMTZaPQOv0bzP+uZy0jJzaGSniZxHrc3RnXtmG5\nu3zmUqIylarm84mM9mx+5wv0DxfPprIF/Ito00qSW1CCaiFaBv6l6f8WKiH+ufg3sdhVh1qmk9US\n0ok1+FPNsQ05NDvy2QjiSCqJxMVOG3nrNG8Ka8dtVEaCA8CvkJPoQrkAO5rYDUinmP9D+wVWGJnP\nZHTMcivwk8T/N5C+JnyNafsZ5MSWA1uB36A52y78xj0n0KeZpu5f5tqL8C+ZrkSO8PjQl2kCr6Ki\nh63IOS9Ho2IZTfUWes6zW8Tdnae3ob0Bll3ou69Cq0Y3olxEGU0Lhxm5EvlFCJCuk6tM+Q7TlzXI\nyM9E894etFz+pJFb6mm76DotvB1fgJJJW5H32om2Md+JEk7W+9iw5PZAW7OMzJrQBRM8Qt+91evQ\nDfMxEvgmumkvIIO9FIW/B+m7ASPJcJQoS1tN+SxKBO0zfb/WqT8aGWNort9MxgLfQJHUftOXp5Ae\npqac827k5F3DehDt+7DMQ7rfjO7pTjQ6LaTvbtIS+TqENJ0MQ4PSdpTnup/KqGaTn/uAP6Pl7bQt\nukXW6eFqx/0IvQNhOJUfV9lPT47XtltFp2QJerjcnDsjS7BAdCLjSv5E1v4E1rdddiBoRCeNMhh1\nCoeQHWe9A2EIFYPtAMaTvVmmFkai0eXuGs9rR558VY59aQXjkeNdArwWeAfKI5TR0lYRqFcnjTJY\ndQqHkB1X8w6ETjRfTAsDG2Um2tlWy4slJqP5WKkJ/Wk2s5HT3YMSil+isnxVFOrRSaMMZp3CIWDH\n1b4D4SuEf/MfqZ82dK+r/bFS5DBhaLZI7kxB2XB3qXIqfTeUxJes5scMNG1Yj5LC89H9vWQgOxUp\nHgPxMogy2g05IlF2DlpKSjqA01D2ONI449HyXA/wM+SQpxHeUhuJtIQJaClkKUpwXYgSI2X6bojq\nRWvhx9G830NEIpECUM07ED6MNlYcRO90jEQikUgkEolEIpFIJBKJRCKRSCRSJP4PSJI3gYHIAeUA\nAAAASUVORK5CYII=\n",
            "text/latex": "$$C R \\frac{d}{d t} u{\\left (t \\right )} = U_{g} \\sin{\\left (\\omega t \\right )} - u{\\left (t \\right )}$$",
            "text/plain": [
              "    d                             \n",
              "C⋅R⋅──(u(t)) = U_g⋅sin(ω⋅t) - u(t)\n",
              "    dt                            "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H9hd1LUaaAci",
        "colab_type": "text"
      },
      "source": [
        "Najprej poskušamo identificirati tip diferencialne enačbe. V ta namen uporabimo funkcijo classify_ode."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IsdGaVyZaAcj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 212
        },
        "outputId": "5da2e90d-a15d-4b35-d129-a655b7c72428"
      },
      "source": [
        "classify_ode(eq, u(t))"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "('1st_linear',\n",
              " 'Bernoulli',\n",
              " 'almost_linear',\n",
              " '1st_power_series',\n",
              " 'lie_group',\n",
              " 'nth_linear_constant_coeff_undetermined_coefficients',\n",
              " 'nth_linear_constant_coeff_variation_of_parameters',\n",
              " '1st_linear_Integral',\n",
              " 'Bernoulli_Integral',\n",
              " 'almost_linear_Integral',\n",
              " 'nth_linear_constant_coeff_variation_of_parameters_Integral')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AiZ7kyzdaAcl",
        "colab_type": "text"
      },
      "source": [
        "Preiskusimo lahko vse zgoraj naštete možne tipe. V našem primeru dobro deluje nth_linear_constant_coeff_undetermined_coefficients"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NRCYKWONaAcm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "6b930ed0-4a23-47ea-f2b5-488e9ed2fac7"
      },
      "source": [
        "dsol = dsolve(eq, u(t),'nth_linear_constant_coeff_undetermined_coefficients')  # rešimo diff enačbo\n",
        "display(dsol)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAAnCAYAAADzVxTtAAAABHNCSVQICAgIfAhkiAAADgZJREFU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\nCw9tAAAAAElFTkSuQmCC\n",
            "text/latex": "$$u{\\left (t \\right )} = - \\frac{C R U_{g} \\omega \\cos{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + C_{1} e^{- \\frac{t}{C R}} + \\frac{U_{g} \\sin{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1}$$",
            "text/plain": [
              "                                  -t                \n",
              "                                  ───               \n",
              "         C⋅R⋅U_g⋅ω⋅cos(ω⋅t)       C⋅R   U_g⋅sin(ω⋅t)\n",
              "u(t) = - ────────────────── + C₁⋅ℯ    + ────────────\n",
              "             2  2  2                     2  2  2    \n",
              "            C ⋅R ⋅ω  + 1                C ⋅R ⋅ω  + 1"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GYhgtNP0aAcw",
        "colab_type": "text"
      },
      "source": [
        "Podobno kot v prejšnjem primeru, zamenjamo konstanto $C_1$ za začetni pogoj, $u(t=0)$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q0OtjldNaAcw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "outputId": "e4d2726a-8d34-43d7-c9f9-569fbadb1641"
      },
      "source": [
        "t0=dsol.args[1].subs({'t':0})\n",
        "eq_init = Eq(u0, t0)  # izrazimo enačbo pri t=0\n",
        "display(eq_init)  # prikažemo i0\n",
        "\n",
        "init_solve=solve(eq_init, C1) # rešimo enačbo za C1\n",
        "\n",
        "display(init_solve)  # prikažemo rešitev\n",
        "final = dsol.subs(C1, init_solve[0]) # v rešitev vstavimo C1 in dobimo končno enačbo\n",
        "final"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMoAAAAlCAYAAAADd3b/AAAABHNCSVQICAgIfAhkiAAABxJJREFU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\nYII=\n",
            "text/latex": "$$u_{0} = - \\frac{C R U_{g} \\omega}{C^{2} R^{2} \\omega^{2} + 1} + C_{1}$$",
            "text/plain": [
              "        C⋅R⋅U_g⋅ω       \n",
              "u₀ = - ──────────── + C₁\n",
              "        2  2  2         \n",
              "       C ⋅R ⋅ω  + 1     "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV8AAAAhCAYAAAB+6qiEAAAABHNCSVQICAgIfAhkiAAACwJJREFU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\nOxwOh8PhcDgcDofD4XA4HA5HH+P/+cIwUTD32nkAAAAASUVORK5CYII=\n",
            "text/latex": "$$\\left [ \\frac{1}{C^{2} R^{2} \\omega^{2} + 1} \\left(C^{2} R^{2} \\omega^{2} u_{0} + C R U_{g} \\omega + u_{0}\\right)\\right ]$$",
            "text/plain": [
              "⎡ 2  2  2                    ⎤\n",
              "⎢C ⋅R ⋅ω ⋅u₀ + C⋅R⋅U_g⋅ω + u₀⎥\n",
              "⎢────────────────────────────⎥\n",
              "⎢         2  2  2            ⎥\n",
              "⎣        C ⋅R ⋅ω  + 1        ⎦"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAApAAAAAnCAYAAAC45Xi0AAAABHNCSVQICAgIfAhkiAAAFGFJREFU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\n",
            "text/latex": "$$u{\\left (t \\right )} = - \\frac{C R U_{g} \\omega \\cos{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{U_{g} \\sin{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} \\left(C^{2} R^{2} \\omega^{2} u_{0} + C R U_{g} \\omega + u_{0}\\right)$$",
            "text/plain": [
              "                                                                             -\n",
              "                                                                             ─\n",
              "                                             ⎛ 2  2  2                    ⎞  C\n",
              "         C⋅R⋅U_g⋅ω⋅cos(ω⋅t)   U_g⋅sin(ω⋅t)   ⎝C ⋅R ⋅ω ⋅u₀ + C⋅R⋅U_g⋅ω + u₀⎠⋅ℯ \n",
              "u(t) = - ────────────────── + ──────────── + ─────────────────────────────────\n",
              "             2  2  2           2  2  2                    2  2  2             \n",
              "            C ⋅R ⋅ω  + 1      C ⋅R ⋅ω  + 1               C ⋅R ⋅ω  + 1         \n",
              "\n",
              "t \n",
              "──\n",
              "⋅R\n",
              "  \n",
              "──\n",
              "  \n",
              "  "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k2NYILoyaAcy",
        "colab_type": "text"
      },
      "source": [
        "Vstavimo začetni pogoj in dobimo končno rešitev:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VEFKFDI1aAcz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 93
        },
        "outputId": "c03d2851-07c4-44c9-eb89-e310174976cb"
      },
      "source": [
        "zacetni_pogoji = {'u0': 0}\n",
        "u2=final.subs(zacetni_pogoji)\n",
        "display((u2))"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZgAAAAqCAYAAACOTk2fAAAABHNCSVQICAgIfAhkiAAADg5JREFU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\nCPwPQtiRvc/D5/IAAAAASUVORK5CYII=\n",
            "text/latex": "$$u{\\left (t \\right )} = - \\frac{C R U_{g} \\omega \\cos{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{C R U_{g} \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{U_{g} \\sin{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1}$$",
            "text/plain": [
              "                                         -t                \n",
              "                                         ───               \n",
              "                                         C⋅R               \n",
              "         C⋅R⋅U_g⋅ω⋅cos(ω⋅t)   C⋅R⋅U_g⋅ω⋅ℯ      U_g⋅sin(ω⋅t)\n",
              "u(t) = - ────────────────── + ────────────── + ────────────\n",
              "             2  2  2            2  2  2         2  2  2    \n",
              "            C ⋅R ⋅ω  + 1       C ⋅R ⋅ω  + 1    C ⋅R ⋅ω  + 1"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "luSwOuJwaAc1",
        "colab_type": "text"
      },
      "source": [
        "Izračunamo še tok kot $i=C\\frac{\\text{d}{{u}_{C}}}{\\text{d}t}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9wUopLmwaAc1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 93
        },
        "outputId": "d3c01104-2a07-4464-ee8e-caf370041e26"
      },
      "source": [
        "i2=symbols('i2')\n",
        "i2=C*u2.rhs.diff(t) # množenje s C in odvodom desne strani enačbe\n",
        "simplify(i2)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZUAAAAqCAYAAAB7sMYvAAAABHNCSVQICAgIfAhkiAAAEFpJREFU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\nEolEIpFIJBKJRCKRSCQSiUQi5fN/wjR8/8UPVkIAAAAASUVORK5CYII=\n",
            "text/latex": "$$\\frac{C U_{g} \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} \\left(\\left(C R \\omega \\sin{\\left (\\omega t \\right )} + \\cos{\\left (\\omega t \\right )}\\right) e^{\\frac{t}{C R}} - 1\\right)$$",
            "text/plain": [
              "        ⎛                              t     ⎞  -t \n",
              "        ⎜                             ───    ⎟  ───\n",
              "        ⎜                             C⋅R    ⎟  C⋅R\n",
              "C⋅U_g⋅ω⋅⎝(C⋅R⋅ω⋅sin(ω⋅t) + cos(ω⋅t))⋅ℯ    - 1⎠⋅ℯ   \n",
              "───────────────────────────────────────────────────\n",
              "                     2  2  2                       \n",
              "                    C ⋅R ⋅ω  + 1                   "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5BEU1yoAaAc3",
        "colab_type": "text"
      },
      "source": [
        "Sedaj lahko ocenimo še pravilnost enačbe. Čeprav je zapis zapleten, lahko ocenimo rešitev pri $CR\\omega >>1$. Najprej izbrišemo 1 in $cos(ut)$, nato še eksponenta, ki se izničita. Ostane nam\n",
        "\n",
        "$\\frac{C U_g \\omega }{C^{2} R^{2} \\omega^{2}} \\left(\\left(C R \\omega \\sin{\\left (\\omega t \\right )}\\right) \\right)$,\n",
        "\n",
        "od koder sledi\n",
        "\n",
        "$\\frac{U_g }{R} \\left(\\left(\\sin{\\left (\\omega t \\right )}\\right) \\right)$,\n",
        "\n",
        "kar je tok, ki ga diktira upornost $R$.\n",
        "\n",
        "Če pa je $CR\\omega << 1$, pa se ohrani cosinusni člen, eksponenta se za velike čase izničita, ostane \n",
        "$\\frac{C U_g \\omega }{C^{2} R^{2} \\omega^{2}+1} \\left(\\left(\\cos{\\left (\\omega t \\right )}\\right) \\right)$ in nato \n",
        "$\\frac{C \\omega U_g}{1} \\left(\\left(\\cos{\\left (\\omega t \\right )}\\right) \\right)$. V tem primeru, npr. nizkih frekvencah, tok skozi vezje diktira \"upornost\" kondenzatorja, ki jo pri izmeničnih signalih imenujemo reaktanca in je enaka $\\frac{1}{\\omega C}$.  \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QO18r9XMaAc4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "53d71dd4-dd7d-4445-93a1-0577b0051aeb"
      },
      "source": [
        "podatki = {C: 5e-5, R: 5e5, Ug: 2, omega:1000} \n",
        "tau=R*C  # časovna konstanta\n",
        "tau2=tau.subs(podatki)  # numeričen izračun konstante z zamenjavo oz. vstavitvijo vrednosti za L in R\n",
        "print('Tau = ',tau2,' s')\n",
        "\n",
        "napetost = lambdify(t,u2.args[1].subs(podatki), 'numpy')  # napetost kot funkcija časa\n",
        "tok = lambdify(t, i2.subs(podatki), 'numpy') # tok kot funkcija časa\n",
        "\n",
        "print('Tok pri 0s: {:g} A'.format(tok(1)))\n",
        "print('Napetost pri 0s: {:g} V'.format(napetost(1)))"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Tau =  25.0000000000000  s\n",
            "Tok pri 0s: 3.30745e-06 A\n",
            "Napetost pri 0s: 3.18755e-05 V\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tGRJN9XpaAc5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "dda63983-bf1e-45b5-d80a-93b9e1557b21"
      },
      "source": [
        "cas = np.linspace(0, 1, 50)\n",
        "\n",
        "def slika():\n",
        "    plt.plot(cas, tok(cas), 'C0', label='Tok [A]')\n",
        "    plt.plot(cas, napetost(cas), 'C1', label='Napetost [V]')\n",
        "    plt.ylabel('Tok [A]  /  Napetost [V]')\n",
        "    plt.legend(loc=(1.01, 0));\n",
        "    plt.show()\n",
        "slika()"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgcAAAD4CAYAAAB4+kXeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lC0O6zDGaAc7",
        "colab_type": "text"
      },
      "source": [
        "Zgornji prikaz ni napačen, problem je le, da sta lahko napetost in tok različnih velikostnih razredov. Zato je bolj primerno izrisati tok in napetost na dveh različnih grafih ali pa na enem grafu ampak z dvema različnima ordinatnima osema. Poleg tega časovni korak ni izbran najbolj ustrezno in ga je potrebno 2zgostiti\". Glej spodaj:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XY6VGTQsaAc8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "239b8cb3-39e9-418c-8405-8a6e76291477"
      },
      "source": [
        "cas = np.linspace(0, 2e-2, 5000)\n",
        "\n",
        "fig, ax1 = plt.subplots()\n",
        "\n",
        "color = 'tab:red'\n",
        "ax1.set_xlabel('Čas (s)')\n",
        "ax1.set_ylabel('Tok (A)', color=color)\n",
        "ax1.plot(cas, tok(cas), color=color)\n",
        "ax1.tick_params(axis='y', labelcolor=color)\n",
        "\n",
        "ax2 = ax1.twinx()  # x os za drugi plot naj bo enaka x osi prvega plota\n",
        "\n",
        "color = 'tab:blue'\n",
        "ax2.set_ylabel('Napetost (V)', color=color)  \n",
        "ax2.plot(cas, napetost(cas), color=color)\n",
        "ax2.tick_params(axis='y', labelcolor=color)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAEICAYAAABlHzwDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZ0mSGmM4S5LUGMNZkqTG/ACh5H6ngFL70QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uim_FKtMaAc-",
        "colab_type": "text"
      },
      "source": [
        "Več:\n",
        "- o uporabi simbolnega računa:\n",
        "    - https://www.southampton.ac.uk/~fangohr/teaching/python/book/html/12-symbolic-computation.html\n",
        "    -"
      ]
    }
  ]
}