5.56   ODE No. 1504

\[ \boxed { \left ( {x}^{2}+2 \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -2\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {x}^{2}+2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,xy \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.108014 (sec), leaf count = 43 \[ \left \{\left \{y(x)\to \frac {c_1 x^2}{2}+\frac {1}{2} i c_2 e^{-i x}-\frac {1}{4} c_3 e^{i x}\right \}\right \} \]

Maple: cpu = 0.171 (sec), leaf count = 18 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\it \_C2}\,\cos \left ( x \right ) +{\it \_C3}\,\sin \left ( x \right ) \right \} \]