\[ a x^2 y''(x)+b x y'(x)+y(x) \left (c x^2+d x+f\right )=0 \] ✓ Mathematica : cpu = 0.183578 (sec), leaf count = 310
\[\left \{\left \{y(x)\to c_1 U\left (-\frac {-\sqrt {c} a-i d \sqrt {a}-\sqrt {c} \sqrt {a^2-2 b a-4 f a+b^2}}{2 a \sqrt {c}},\frac {\sqrt {a^2-2 b a-4 f a+b^2}}{a}+1,\frac {2 i \sqrt {c} x}{\sqrt {a}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {a^2-2 a b-4 a f+b^2}+a-b\right )-2 i \sqrt {a} \sqrt {c} x}{2 a}\right )+c_2 L_{\frac {-\sqrt {c} a-i d \sqrt {a}-\sqrt {c} \sqrt {a^2-2 b a-4 f a+b^2}}{2 a \sqrt {c}}}^{\frac {\sqrt {a^2-2 b a-4 f a+b^2}}{a}}\left (\frac {2 i \sqrt {c} x}{\sqrt {a}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {a^2-2 a b-4 a f+b^2}+a-b\right )-2 i \sqrt {a} \sqrt {c} x}{2 a}\right )\right \}\right \}\] ✓ Maple : cpu = 0.543 (sec), leaf count = 106
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {b}{2\,a}}} \left ( {{\sl M}_{{-{\frac {i}{2}}d{\frac {1}{\sqrt {a}}}{\frac {1}{\sqrt {c}}}},\,{\frac {1}{2\,a}\sqrt {{a}^{2}+ \left ( -2\,b-4\,f \right ) a+{b}^{2}}}}\left ({2\,ix\sqrt {c}{\frac {1}{\sqrt {a}}}}\right )}{\it \_C1}+{{\sl W}_{{-{\frac {i}{2}}d{\frac {1}{\sqrt {a}}}{\frac {1}{\sqrt {c}}}},\,{\frac {1}{2\,a}\sqrt {{a}^{2}+ \left ( -2\,b-4\,f \right ) a+{b}^{2}}}}\left ({2\,ix\sqrt {c}{\frac {1}{\sqrt {a}}}}\right )}{\it \_C2} \right ) \right \} \]