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 = 0.0175744 (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 = 0.073 (sec), leaf count = 41

\[\left \{y \left (x \right ) = \frac {i c_{2} \sqrt {\pi }\, \sqrt {2}\, x +\left (-c_{2} \pi \erf \left (\frac {i \sqrt {2}\, x}{2}\right )+c_{1}\right ) {\mathrm e}^{-\frac {x^{2}}{2}}}{x^{2}}\right \}\]