4.192   ODE No. 1192

\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) =0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 10.168291 (sec), leaf count = 39 \[ \left \{\left \{y(x)\to c_2 e^{-x} \int _1^x e^{K[1]-\frac {1}{K[1]}} \, dK[1]+c_1 e^{-x}\right \}\right \} \]

Maple: cpu = 0.109 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}}{\it HeunD} \left ( 4,3,-8,5,{\frac {x-1}{1+x}} \right ) \sqrt {x}+{\it \_C2}\,{ {\rm e}^{-{x}^{-1}}}{\it HeunD} \left ( -4,3,-8,5,{\frac {x-1}{1+x}} \right ) \sqrt {x} \right \} \]