2.1192   ODE No. 1192

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

\[ x^2 y''(x)+\left (x^2-1\right ) y'(x)-y(x)=0 \] Mathematica : cpu = 10.8161 (sec), leaf count = 34

\[\left \{\left \{y(x)\to e^{-x} \left (c_2 \int _1^x e^{K[1]-\frac {1}{K[1]}} \, dK[1]+c_1\right )\right \}\right \}\]

Maple : cpu = 0.132 (sec), leaf count = 51

\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {\it HeunD} \left ( -4,3,-8,5,{\frac {x-1}{1+x}} \right ) {{\rm e}^{-{x}^{-1}}}{\it \_C2}+{{\rm e}^{-x}}{\it HeunD} \left ( 4,3,-8,5,{\frac {x-1}{1+x}} \right ) {\it \_C1} \right ) \right \} \]