2.1191   ODE No. 1191

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

\[ x^2 y''(x)+x^2 y'(x)-2 y(x)=0 \] Mathematica : cpu = 0.0108513 (sec), leaf count = 72

\[\left \{\left \{y(x)\to \frac {e^{-x/2} \left (2 \left (2 c_1+i c_2 x\right ) \sinh \left (\frac {x}{2}\right )-2 \left (c_1 x+2 i c_2\right ) \cosh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x} \sqrt {x}}\right \}\right \}\]

Maple : cpu = 0.017 (sec), leaf count = 23

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\, \left ( x+2 \right ) {{\rm e}^{-x}}+{\it \_C1}\, \left ( x-2 \right ) }{x}} \right \} \]