\[ (a x+b) y'(x)+y(x) (c x+d)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0379683 (sec), leaf count = 168
\[\left \{\left \{y(x)\to c_1 e^{-\frac {1}{2} x \sqrt {a^2-4 c}-\frac {a x}{2}} U\left (-\frac {-a b-\sqrt {a^2-4 c} b+2 d}{2 \sqrt {a^2-4 c}},b,\sqrt {a^2-4 c} x\right )+c_2 e^{-\frac {1}{2} x \sqrt {a^2-4 c}-\frac {a x}{2}} L_{\frac {-a b-\sqrt {a^2-4 c} b+2 d}{2 \sqrt {a^2-4 c}}}^{b-1}\left (\sqrt {a^2-4 c} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.215 (sec), leaf count = 109
\[y \relax (x ) = {\mathrm e}^{-\frac {x \left (a +\sqrt {a^{2}-4 c}\right )}{2}} \left (\KummerM \left (\frac {b \sqrt {a^{2}-4 c}+a b -2 d}{2 \sqrt {a^{2}-4 c}}, b , \sqrt {a^{2}-4 c}\, x \right ) c_{1}+\KummerU \left (\frac {b \sqrt {a^{2}-4 c}+a b -2 d}{2 \sqrt {a^{2}-4 c}}, b , \sqrt {a^{2}-4 c}\, x \right ) c_{2}\right )\]