ODE No. 1039

\[ y''(x)+x y'(x)+y(x)=0 \] Mathematica : cpu = 0.009149 (sec), leaf count = 47

DSolve[y[x] + x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \sqrt {\frac {\pi }{2}} c_1 e^{-\frac {x^2}{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+c_2 e^{-\frac {x^2}{2}}\right \}\right \}\] Maple : cpu = 0.019 (sec), leaf count = 25

dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x)=0,y(x))
 

\[y \left (x \right ) = \left (\erf \left (\frac {i \sqrt {2}\, x}{2}\right ) c_{1}+c_{2}\right ) {\mathrm e}^{-\frac {x^{2}}{2}}\]