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 = 0.0218425 (sec), leaf count = 59

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

Maple : cpu = 0.055 (sec), leaf count = 41

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