\[ (a x+b) y'(x)+y(x) (c x+d)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0646185 (sec), leaf count = 135
\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x \left (\sqrt {a^2-4 c}+a\right )} \left (c_1 U\left (\frac {a b+\sqrt {a^2-4 c} b-2 d}{2 \sqrt {a^2-4 c}},b,\sqrt {a^2-4 c} x\right )+c_2 L_{-\frac {a b+\sqrt {a^2-4 c} b-2 d}{2 \sqrt {a^2-4 c}}}^{b-1}\left (\sqrt {a^2-4 c} x\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.286 (sec), leaf count = 109
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2} \left ( a+\sqrt {{a}^{2}-4\,c} \right ) }}} \left ( {{\sl M}\left ({\frac {1}{2} \left ( b\sqrt {{a}^{2}-4\,c}+ab-2\,d \right ) {\frac {1}{\sqrt {{a}^{2}-4\,c}}}},\,b,\,\sqrt {{a}^{2}-4\,c}x\right )}{\it \_C1}+{{\sl U}\left ({\frac {1}{2} \left ( b\sqrt {{a}^{2}-4\,c}+ab-2\,d \right ) {\frac {1}{\sqrt {{a}^{2}-4\,c}}}},\,b,\,\sqrt {{a}^{2}-4\,c}x\right )}{\it \_C2} \right ) \right \} \]