\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 3\,{x}^{2}+2\,n-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.010001 (sec), leaf count = 45 \[ \left \{\left \{y(x)\to c_1 e^{\frac {x^2}{2}} H_n(x)+c_2 e^{\frac {x^2}{2}} \, _1F_1\left (-\frac {n}{2};\frac {1}{2};x^2\right )\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2} }}}{{\sl M}\left (-{\frac {n}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,{x} ^{2}\right )}x+{\it \_C2}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}}{{\sl U} \left (-{\frac {n}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,{x}^{2} \right )}x \right \} \]