\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{a}^{2}{x}^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.029004 (sec), leaf count = 57 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {a x^2}{2}-\sqrt {a} x}+\frac {c_2 e^{\sqrt {a} x-\frac {a x^2}{2}}}{2 \sqrt {a}}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {x}{2} \left ( ax-2\,\sqrt {a} \right ) }}}+{\it \_C2}\,{{\rm e}^{-{\frac {x}{ 2} \left ( ax+2\,\sqrt {a} \right ) }}} \right \} \]