2.1209   ODE No. 1209

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

\[ \left (x^2+2\right ) x y'(x)+x^2 y''(x)+\left (x^2-2\right ) y(x)=0 \] Mathematica : cpu = 0.0155164 (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 = 0.075 (sec), leaf count = 40

\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( \left ( \pi \,{\it Erf} \left ( {\frac {i}{2}}\sqrt {2}x \right ) {\it \_C2}+{\it \_C1} \right ) {{\rm e}^{-{\frac {{x}^{2}}{2}}}}-i\sqrt {\pi }\sqrt {2}{\it \_C2}\,x \right ) } \right \} \]