4.176   ODE No. 1176

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

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

Mathematica: cpu = 0.017502 (sec), leaf count = 33 \[ \left \{\left \{y(x)\to c_1 e^{-i x} x-\frac {1}{2} i c_2 e^{i x} x\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x\sin \left ( x \right ) +{\it \_C2}\,\cos \left ( x \right ) x \right \} \]