Differential_Equation_const_2nd_order_191117.ipynb

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    "#スクリプト部分の表示制御\n",
    "#https://qiita.com/simonritchie/items/d7dccb798f0b9c8b1ec5\n",
    "#の記事を用いて作成しました．大変有り難うございます．\n",
    "\n",
    "from IPython.display import HTML\n",
    "\n",
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    "        switch_btn.text(\"スクリプトを表示する\");\n",
    "    }else{\n",
    "        $(\"div.input\").show();\n",
    "        code_show = true;\n",
    "        switch_btn.text(\"スクリプトを非表示にする\");\n",
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    "\n",
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    "##  定数係数2階線形同次微分方程式プログラム\n",
    "\n",
    "定数係数の$2$階線形同次微分方程式をインタラクティブに解くプログラムです．\n",
    "\n",
    "実行すると，$a,b,c$に数値を入力するボックスがプログラム部分の直後に現れるので，指定して下さい．定数係数2階線形同次微分方程式$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=0$を定式化できます．Typeで「微分方程式の一般解」を選ぶと，一般解が即座に表示されます．「特性方程式とその解」を選ぶと，対応する特性方程式とその解が表示されます．「全て」を選ぶと，対応する特性方程式とその解，微分方程式の一般解が順に表示されます．\n",
    "\n",
    "【入力上の注意】．\n",
    "- $\\frac{a}{b}$はa/bのように書きます．"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "\n",
    "from ipywidgets import interact\n",
    "# インタラクティブ画面が出ない場合　：　「jupyter nbextension enable --py widgetsnbextension」をターミナル等で一度実行．\n",
    "# Try jupyter[https://jupyter.org/try]上では問題なく動作．\n",
    "\n",
    "from IPython.display import Math"
   ]
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   "source": [
    "# 1変数関数の微分をインタラクティブに解きます．\n",
    "x ,a, b, c = symbols('x a b c')\n",
    "y = symbols('y' ,cls=Function)\n",
    "\n",
    "@interact(a='1', b='3', c='2', Type=['微分方程式の表示', '微分方程式の一般解', '特性方程式とその解', '全て'])\n",
    "def f(a,b,c, Type):\n",
    "    # sympy形式の数式への変換\n",
    "    a = sympify(a)\n",
    "    b = sympify(b)\n",
    "    c = sympify(c)\n",
    "    \n",
    "    diffeq = Eq( a*y(x).diff(x, 2) + b*y(x).diff(x, 1) + c*y(x) , 0 )\n",
    "    display( Math(r'微分方程式：%s' % ( latex(diffeq) ) ) )\n",
    "    if(Type!='微分方程式の表示'):\n",
    "        if(Type!='微分方程式の一般解'):\n",
    "            display( Math(r'特性方程式：%s\\lambda^{2}+%s\\lambda+%s=0' % ( latex(a), latex(b), latex(c) ) ) )\n",
    "        if(Type!='微分方程式の一般解'):\n",
    "            display( Math(r'特性方程式の解：\\lambda=%s' % ( latex(solve(a*x**2+b*x+c,x)) ) ) )\n",
    "        if(Type!='特性方程式とその解'):\n",
    "            display( Math(r'微分方程式の一般解：%s' % ( latex(dsolve( diffeq, y(x) )) ) ) )"
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