4.40   ODE No. 1040

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

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

Mathematica: cpu = 0.030004 (sec), leaf count = 53 \[ \left \{\left \{y(x)\to c_1 x-\frac {1}{2} c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } e^{\frac {x^2}{2}} x \text {erf}\left (\frac {x}{\sqrt {2}}\right )+2\right )\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 34 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\, \left ( \pi \,{ \it Erf} \left ( {\frac {x\sqrt {2}}{2}} \right ) x+\sqrt {2}\sqrt {\pi }{{\rm e}^{-{\frac {{x}^{2}}{2}}}} \right ) \right \} \]