\[ (a+b x) y'(x)+2 a x y''(x)+c y(x)=0 \] ✓ Mathematica : cpu = 0.0289427 (sec), leaf count = 93
\[\left \{\left \{y(x)\to c_1 e^{\frac {a \log (x)-b x}{2 a}} U\left (-\frac {c-b}{b},\frac {3}{2},\frac {b x}{2 a}\right )+c_2 e^{\frac {a \log (x)-b x}{2 a}} L_{\frac {c-b}{b}}^{\frac {1}{2}}\left (\frac {b x}{2 a}\right )\right \}\right \}\] ✓ Maple : cpu = 0.231 (sec), leaf count = 57
\[\left \{y \left (x \right ) = \left (c_{1} \KummerM \left (\frac {b -c}{b}, \frac {3}{2}, \frac {b x}{2 a}\right )+c_{2} \KummerU \left (\frac {b -c}{b}, \frac {3}{2}, \frac {b x}{2 a}\right )\right ) \sqrt {x}\, {\mathrm e}^{-\frac {b x}{2 a}}\right \}\]