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 = 0.0079458 (sec), leaf count = 110

\[\left \{\left \{y(x)\to \frac {2 c_2 e^{\frac {1}{2} (\log (x)-x)} \left (i \sinh \left (\frac {x}{2}\right )-\frac {2 i \cosh \left (\frac {x}{2}\right )}{x}\right )}{\sqrt {\pi } \sqrt {-i x}}+\frac {2 c_1 e^{\frac {1}{2} (\log (x)-x)} \left (\frac {2 \sinh \left (\frac {x}{2}\right )}{x}-\cosh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}}\right \}\right \}\] Maple : cpu = 0.041 (sec), leaf count = 23

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