\[ (a+b x) y'(x)+2 a x y''(x)+c y(x)=0 \] ✓ Mathematica : cpu = 0.0259795 (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 = 0.545 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {bx}{2\,a}}}}\sqrt {x} \left ( {{\sl U}\left ({\frac {b-c}{b}},\,{\frac {3}{2}},\,{\frac {bx}{2\,a}}\right )}{\it \_C2}+{{\sl M}\left ({\frac {b-c}{b}},\,{\frac {3}{2}},\,{\frac {bx}{2\,a}}\right )}{\it \_C1} \right ) \right \} \]