2.1040   ODE No. 1040

\[ y''(x)+x y'(x)-y(x)=0 \] Mathematica : cpu = 0.039041 (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 = 0.045 (sec), leaf count = 33


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