4.209   ODE No. 1209

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

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

Mathematica: cpu = 0.020002 (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 = 0.047 (sec), leaf count = 48 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{{x}^{2}}{{\rm e}^{-{ \frac {{x}^{2}}{2}}}}}+{\frac {{\it \_C2}}{{x}^{2}} \left ( -ix\sqrt { \pi }\sqrt {2}+{{\rm e}^{-{\frac {{x}^{2}}{2}}}}\pi \,{\it Erf} \left ( {\frac {i}{2}}\sqrt {2}x \right ) \right ) } \right \} \]