\[ -n y(x)+y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.0087322 (sec), leaf count = 61
\[\left \{\left \{y(x)\to c_1 e^{-\frac {x^2}{2}} H_{-n-1}\left (\frac {x}{\sqrt {2}}\right )+c_2 e^{-\frac {x^2}{2}} \, _1F_1\left (\frac {n+1}{2};\frac {1}{2};\frac {x^2}{2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.147 (sec), leaf count = 41
\[\left \{y \left (x \right ) = \left (c_{1} \KummerM \left (\frac {n}{2}+1, \frac {3}{2}, \frac {x^{2}}{2}\right )+c_{2} \KummerU \left (\frac {n}{2}+1, \frac {3}{2}, \frac {x^{2}}{2}\right )\right ) x \,{\mathrm e}^{-\frac {x^{2}}{2}}\right \}\]