{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.0 (Python 3.5.2-64-bit) (ground types: python)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at http://docs.sympy.org/1.0/\n"
     ]
    }
   ],
   "source": [
    "init_session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "r, theta, phi, kappa, alpha = symbols('r theta phi kappa alpha')\n",
    "R, Theta = symbols('R Theta', cls=Function)\n",
    "u = f(r, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq = 1/r**2*diff(r**2*u.diff(r), r) + 1/(r**2*sin(theta))*diff(sin(theta)*u.diff(theta), theta) + kappa**2*u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "aux = expand(r**2*eq.subs(f(r, theta), R(r)*Theta(theta)).doit()/(R(r)*Theta(theta)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VGijPO5hfJGAxlfnPM4ieYXArlCkRNulU0UijIVTq2O0aBi+irUTNGKtQX1DYi2iu/4GC\n9QpU2cynnLkTUDQN26HXTmhg15WoE/pl4DLKE9P1kj5ghNlXy7Yo+zw5ZRJqu0wyk9bpwH3NNadj\nSaqj17CSNP4X0M0a5l2vltqX6+n/Csoy1Ma4GkX5OMYA3wf+3WyjOpCkOnoNK0njfwHdrGHe9cq7\nfR6Px+PxeDwej8fj8Xg8Hk8j/B92OUDfFBIXzwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\kappa^{2} r^{2} + \\frac{r^{2} \\frac{d^{2}}{d r^{2}}  R{\\left (r \\right )}}{R{\\left (r \\right )}} + \\frac{2 r \\frac{d}{d r} R{\\left (r \\right )}}{R{\\left (r \\right )}} + \\frac{\\frac{d^{2}}{d \\theta^{2}}  \\Theta{\\left (\\theta \\right )}}{\\Theta{\\left (\\theta \\right )}} + \\frac{\\cos{\\left (\\theta \\right )} \\frac{d}{d \\theta} \\Theta{\\left (\\theta \\right )}}{\\Theta{\\left (\\theta \\right )} \\sin{\\left (\\theta \\right )}}$$"
      ],
      "text/plain": [
       "             2                          2                        \n",
       "         2  d                          d                         \n",
       "        r ⋅───(R(r))       d          ───(Θ(θ))          d       \n",
       "             2         2⋅r⋅──(R(r))     2         cos(θ)⋅──(Θ(θ))\n",
       " 2  2      dr              dr         dθ                 dθ      \n",
       "κ ⋅r  + ──────────── + ──────────── + ───────── + ───────────────\n",
       "            R(r)           R(r)          Θ(θ)       Θ(θ)⋅sin(θ)  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATkAAAArCAYAAAADiP/VAAAABHNCSVQICAgIfAhkiAAADRdJREFU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\nrkJggg==\n",
      "text/latex": [
       "$$- \\alpha^{2} \\Theta{\\left (\\theta \\right )} + \\frac{d^{2}}{d \\theta^{2}}  \\Theta{\\left (\\theta \\right )} + \\frac{\\frac{d}{d \\theta} \\Theta{\\left (\\theta \\right )}}{\\sin{\\left (\\theta \\right )}} \\cos{\\left (\\theta \\right )}$$"
      ],
      "text/plain": [
       "                               d       \n",
       "              2         cos(θ)⋅──(Θ(θ))\n",
       "   2         d                 dθ      \n",
       "- α ⋅Θ(θ) + ───(Θ(θ)) + ───────────────\n",
       "              2              sin(θ)    \n",
       "            dθ                         "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1 = Theta(theta).diff(theta, 2) + cos(theta)/sin(theta)*Theta(theta).diff(theta) - alpha**2*Theta(theta)\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAAmCAYAAAA2jntiAAAABHNCSVQICAgIfAhkiAAACP5JREFU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\nFEVRFEVRFEVRFEVRFEVRIuJ9Nvm6poR4HbcAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\alpha^{2} R{\\left (r \\right )} + \\kappa^{2} r^{2} R{\\left (r \\right )} + r^{2} \\frac{d^{2}}{d r^{2}}  R{\\left (r \\right )} + 2 r \\frac{d}{d r} R{\\left (r \\right )}$$"
      ],
      "text/plain": [
       "                            2                     \n",
       " 2         2  2         2  d              d       \n",
       "α ⋅R(r) + κ ⋅r ⋅R(r) + r ⋅───(R(r)) + 2⋅r⋅──(R(r))\n",
       "                            2             dr      \n",
       "                          dr                      "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2 = expand(aux - eq1/Theta(theta))\n",
    "eq2 = expand(eq2*R(r))\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha**2*R(r) + kappa**2*r**2*R(r) + r**2*Derivative(R(r), r, r) + 2*r*Derivative(R(r), r)\n"
     ]
    }
   ],
   "source": [
    "print(eq2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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