\[ y(x) \left (a b x+c x^2+d\right )+x (2 a x+b) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0904464 (sec), leaf count = 120
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (-2 a x-(b-1) \log (x))} J_{\frac {1}{2} \sqrt {b^2-2 b-4 d+1}}\left (-i \sqrt {a^2-c} x\right )+c_2 e^{\frac {1}{2} (-2 a x-(b-1) \log (x))} Y_{\frac {1}{2} \sqrt {b^2-2 b-4 d+1}}\left (-i \sqrt {a^2-c} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.146 (sec), leaf count = 76
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-ax}}{x}^{-{\frac {b}{2}}+{\frac {1}{2}}} \left ( {{\sl Y}_{{\frac {1}{2}\sqrt {{b}^{2}-2\,b-4\,d+1}}}\left (\sqrt {-{a}^{2}+c}x\right )}{\it \_C2}+{{\sl J}_{{\frac {1}{2}\sqrt {{b}^{2}-2\,b-4\,d+1}}}\left (\sqrt {-{a}^{2}+c}x\right )}{\it \_C1} \right ) \right \} \]