\[ (a+b x) y'(x)+2 a x y''(x)+c y(x)=0 \] ✓ Mathematica : cpu = 0.0484302 (sec), leaf count = 70
\[\left \{\left \{y(x)\to \sqrt {x} e^{-\frac {b x}{2 a}} \left (c_1 U\left (1-\frac {c}{b},\frac {3}{2},\frac {b x}{2 a}\right )+c_2 L_{\frac {c}{b}-1}^{\frac {1}{2}}\left (\frac {b x}{2 a}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.117 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) =\sqrt {x}{{\rm e}^{-{\frac {bx}{2\,a}}}} \left ( {{\sl U}\left ({\frac {b-c}{b}},\,{\frac {3}{2}},\,{\frac {bx}{2\,a}}\right )}{\it \_C2}+{{\sl M}\left ({\frac {b-c}{b}},\,{\frac {3}{2}},\,{\frac {bx}{2\,a}}\right )}{\it \_C1} \right ) \right \} \]