\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( n+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.008501 (sec), leaf count = 55 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {x^2}{2}} H_n\left (\frac {x}{\sqrt {2}}\right )+c_2 e^{-\frac {x^2}{2}} \, _1F_1\left (-\frac {n}{2};\frac {1}{2};\frac {x^2}{2}\right )\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {{x}^{2}}{2 }}}}{{\sl M}\left (-{\frac {n}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,{ \frac {{x}^{2}}{2}}\right )}x+{\it \_C2}\,{{\rm e}^{-{\frac {{x}^{2}}{2 }}}}{{\sl U}\left (-{\frac {n}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,{ \frac {{x}^{2}}{2}}\right )}x \right \} \]