4.208   ODE No. 1208

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

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

Mathematica: cpu = 0.037005 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to \frac {c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } e^{\frac {x^2}{2}} \text {erf}\left (\frac {x}{\sqrt {2}}\right )-2 x\right )}{2 x}+\frac {c_1}{x}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{x}}+{\frac {{\it \_C2 }}{x} \left ( -\sqrt {\pi }\sqrt {2}{\it Erf} \left ( {\frac {x\sqrt {2} }{2}} \right ) +2\,x{{\rm e}^{-1/2\,{x}^{2}}} \right ) } \right \} \]