\[ a x y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0162794 (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 = 0.164 (sec), leaf count = 58
\[\left \{y \left (x \right ) = \left (c_{1} \KummerM \left (\frac {2 a -b}{2 a}, \frac {3}{2}, \frac {a \,x^{2}}{2}\right )+c_{2} \KummerU \left (\frac {2 a -b}{2 a}, \frac {3}{2}, \frac {a \,x^{2}}{2}\right )\right ) x \,{\mathrm e}^{-\frac {a \,x^{2}}{2}}\right \}\]