\[ -n y(x)+y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.0055813 (sec), leaf count = 61
DSolve[-(n*y[x]) + x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-\frac {x^2}{2}} \operatorname {HermiteH}\left (-n-1,\frac {x}{\sqrt {2}}\right )+c_2 e^{-\frac {x^2}{2}} \operatorname {Hypergeometric1F1}\left (\frac {n+1}{2},\frac {1}{2},\frac {x^2}{2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.085 (sec), leaf count = 41
dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)-n*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {x^{2}}{2}} x \left (\operatorname {KummerU}\left (\frac {n}{2}+1, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_{2}+\operatorname {KummerM}\left (\frac {n}{2}+1, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_{1}\right )\]