\[ (n+1) y(x)+y''(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 0.00998801 (sec), leaf count = 47
\[\left \{\left \{y(x)\to e^{-\frac {x^2}{2}} \left (c_1 H_n\left (\frac {x}{\sqrt {2}}\right )+c_2 \, _1F_1\left (-\frac {n}{2};\frac {1}{2};\frac {x^2}{2}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.072 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {{x}^{2}}{2}}}}x \left ( {{\sl M}\left (-{\frac {n}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,{\frac {{x}^{2}}{2}}\right )}{\it \_C1}+{{\sl U}\left (-{\frac {n}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,{\frac {{x}^{2}}{2}}\right )}{\it \_C2} \right ) \right \} \]