\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( {a}^{2}{x}^{2}+a \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.019502 (sec), leaf count = 43 \[ \left \{\left \{y(x)\to c_1 D_{-1}\left (\sqrt {2} \sqrt {a} x\right )+c_2 D_0\left (i \sqrt {2} \sqrt {a} x\right )\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {a{x}^{2}}{2 }}}}+{\it \_C2}\,{{\rm e}^{{\frac {a{x}^{2}}{2}}}}{\it Erf} \left ( \sqrt {a}x \right ) \right \} \]