2.1150   ODE No. 1150

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

\[ x^2 y''(x)+\left (x^2-2\right ) y(x)=0 \] Mathematica : cpu = 0.0068577 (sec), leaf count = 53

\[\left \{\left \{y(x)\to \sqrt {\frac {2}{\pi }} c_2 \left (-\sin (x)-\frac {\cos (x)}{x}\right )+\sqrt {\frac {2}{\pi }} c_1 \left (\frac {\sin (x)}{x}-\cos (x)\right )\right \}\right \}\] Maple : cpu = 0.161 (sec), leaf count = 27

\[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it \_C1}\,x+{\it \_C2} \right ) \cos \left ( x \right ) +\sin \left ( x \right ) \left ( {\it \_C2}\,x-{\it \_C1} \right ) }{x}} \right \} \]