\[ a x y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.022236 (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 = 0.095 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {a{x}^{2}}{2}}}}{{\sl M}\left ({\frac {2\,a-b}{2\,a}},\,{\frac {3}{2}},\,{\frac {a{x}^{2}}{2}}\right )}x+{\it \_C2}\,{{\rm e}^{-{\frac {a{x}^{2}}{2}}}}{{\sl U}\left ({\frac {2\,a-b}{2\,a}},\,{\frac {3}{2}},\,{\frac {a{x}^{2}}{2}}\right )}x \right \} \]