\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.006501 (sec), leaf count = 31 \[ \left \{\left \{y(x)\to c_1 H_{\frac {a}{2}}(x)+c_2 \, _1F_1\left (-\frac {a}{4};\frac {1}{2};x^2\right )\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}\left ({\frac {1}{2}}- {\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2}\right )}x+{\it \_C2}\,{ {\sl U}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2} \right )}x \right \} \]