2.1209   ODE No. 1209

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

\[ x^2 y''(x)+\left (x^2+2\right ) x y'(x)+\left (x^2-2\right ) y(x)=0 \] Mathematica : cpu = 0.0220125 (sec), leaf count = 67

\[\left \{\left \{y(x)\to \frac {c_1 e^{-\frac {x^2}{2}} \left (e^{\frac {x^2}{2}} x-\sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right )\right )}{x^2}+\frac {c_2 e^{-\frac {x^2}{2}}}{x^2}\right \}\right \}\]

Maple : cpu = 0.054 (sec), leaf count = 49

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{{x}^{2}}{{\rm e}^{-{\frac {{x}^{2}}{2}}}}}+{\frac {{\it \_C2}}{{x}^{2}} \left ( ix\sqrt {\pi }\sqrt {2}-{\it Erf} \left ( {\frac {i}{2}}\sqrt {2}x \right ) \pi \,{{\rm e}^{-{\frac {{x}^{2}}{2}}}} \right ) } \right \} \]