4.150   ODE No. 1150

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

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

Mathematica: cpu = 0.009001 (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 = 0.063 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( \cos \left ( x \right ) x-\sin \left ( x \right ) \right ) }{x}}+{\frac {{\it \_C2}\, \left ( \cos \left ( x \right ) +x\sin \left ( x \right ) \right ) }{x}} \right \} \]