\[ a x y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0224562 (sec), leaf count = 67
\[\left \{\left \{y(x)\to e^{-\frac {a x^2}{2}} \left (c_1 H_{\frac {b}{a}-1}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )+c_2 \, _1F_1\left (\frac {a-b}{2 a};\frac {1}{2};\frac {a x^2}{2}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.082 (sec), leaf count = 58
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {a{x}^{2}}{2}}}}x \left ( {{\sl M}\left ({\frac {2\,a-b}{2\,a}},\,{\frac {3}{2}},\,{\frac {a{x}^{2}}{2}}\right )}{\it \_C1}+{{\sl U}\left ({\frac {2\,a-b}{2\,a}},\,{\frac {3}{2}},\,{\frac {a{x}^{2}}{2}}\right )}{\it \_C2} \right ) \right \} \]