\[ (a+b x) y'(x)+2 a x y''(x)+c y(x)=0 \] ✓ Mathematica : cpu = 0.0477128 (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 = 0.114 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {bx}{2\,a}}}}{{\sl M}\left ({\frac {b-c}{b}},\,{\frac {3}{2}},\,{\frac {bx}{2\,a}}\right )}\sqrt {x}+{\it \_C2}\,{{\rm e}^{-{\frac {bx}{2\,a}}}}{{\sl U}\left ({\frac {b-c}{b}},\,{\frac {3}{2}},\,{\frac {bx}{2\,a}}\right )}\sqrt {x} \right \} \]