\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 4\,{x}^{2}+2 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.013502 (sec), leaf count = 27 \[ \left \{\left \{y(x)\to c_1 e^{-x^2}+c_2 e^{-x^2} x\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 22 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{x}^{2}}}+{\it \_C2}\,x{{\rm e}^{-{x}^{2}}} \right \} \]