\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.008001 (sec), leaf count = 39 \[ \left \{\left \{y(x)\to c_1 H_{-a}\left (\frac {x}{\sqrt {2}}\right )+c_2 \, _1F_1\left (\frac {a}{2};\frac {1}{2};\frac {x^2}{2}\right )\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}\left ({\frac {1}{2}}+ {\frac {a}{2}},\,{\frac {3}{2}},\,{\frac {{x}^{2}}{2}}\right )}x+{\it \_C2}\,{{\sl U}\left ({\frac {1}{2}}+{\frac {a}{2}},\,{\frac {3}{2}},\, {\frac {{x}^{2}}{2}}\right )}x \right \} \]