4.43   ODE No. 1043

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

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

Mathematica: cpu = 0.044506 (sec), leaf count = 69 \[ \left \{\left \{y(x)\to \frac {1}{4} c_2 \left (\sqrt {2 \pi } x^2 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-\sqrt {2 \pi } \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-2 e^{\frac {x^2}{2}} x\right )+c_1 \left (x^2-1\right )\right \}\right \} \]

Maple: cpu = 0.140 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( -2\,x{{\rm e}^{1/2\,{ x}^{2}}}+{\it erfi} \left ( {\frac {x\sqrt {2}}{2}} \right ) \sqrt {\pi }\sqrt {2} \left ( x-1 \right ) \left ( 1+x \right ) \right ) +{\it \_C2} \, \left ( {x}^{2}-1 \right ) \right \} \]