\[ a x^2 y''(x)+b x y'(x)+y(x) \left (c x^2+d x+f\right )=0 \] ✓ Mathematica : cpu = 0.195363 (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 = 0.279 (sec), leaf count = 106
\[\left \{y \left (x \right ) = \left (c_{1} \WhittakerM \left (-\frac {i d}{2 \sqrt {a}\, \sqrt {c}}, \frac {\sqrt {a^{2}+b^{2}+\left (-2 b -4 f \right ) a}}{2 a}, \frac {2 i \sqrt {c}\, x}{\sqrt {a}}\right )+c_{2} \WhittakerW \left (-\frac {i d}{2 \sqrt {a}\, \sqrt {c}}, \frac {\sqrt {a^{2}+b^{2}+\left (-2 b -4 f \right ) a}}{2 a}, \frac {2 i \sqrt {c}\, x}{\sqrt {a}}\right )\right ) x^{-\frac {b}{2 a}}\right \}\]