\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +by \left ( x \right ) =0} \]
Mathematica: cpu = 0.020503 (sec), leaf count = 78 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {a x^2}{2}} H_{\frac {b-a}{a}}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )+c_2 e^{-\frac {a x^2}{2}} \, _1F_1\left (-\frac {b-a}{2 a};\frac {1}{2};\frac {a x^2}{2}\right )\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 65 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {a{x}^{2}}{ 2}}}}{{\sl M}\left ({\frac {2\,a-b}{2\,a}},\,{\frac {3}{2}},\,{\frac {a {x}^{2}}{2}}\right )}x+{\it \_C2}\,{{\rm e}^{-{\frac {a{x}^{2}}{2}}}}{ {\sl U}\left ({\frac {2\,a-b}{2\,a}},\,{\frac {3}{2}},\,{\frac {a{x}^{2 }}{2}}\right )}x \right \} \]