4.39   ODE No. 1039

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

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

Mathematica: cpu = 0.011501 (sec), leaf count = 47 \[ \left \{\left \{y(x)\to \sqrt {\frac {\pi }{2}} c_1 e^{-\frac {x^2}{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+c_2 e^{-\frac {x^2}{2}}\right \}\right \} \]

Maple: cpu = 0.015 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={{\it Erf} \left ( {\frac {i}{2}}\sqrt {2} x \right ) {\it \_C1} \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^ {-1}}+{{\it \_C2} \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{-1 }} \right \} \]