\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\,ax{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +3\,{a}^{2}{x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{a}^{3}{x}^{3}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.027003 (sec), leaf count = 72 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {a x^2}{2}}+c_2 e^{-\frac {a x^2}{2}-\sqrt {3} \sqrt {a} x}+c_3 e^{\sqrt {3} \sqrt {a} x-\frac {a x^2}{2}}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {a{x}^{2}}{2}}}} \left ( {\it \_C1}+{\it \_C2}\,{{\rm e}^{\sqrt {3}\sqrt {a}x}}+{\it \_C3}\,{{\rm e}^{-\sqrt {3}\sqrt {a}x}} \right ) \right \} \]