\[ a x^2 y''(x)+b x y'(x)+y(x) \left (c x^2+d x+f\right )=0 \] ✓ Mathematica : cpu = 0.278479 (sec), leaf count = 229
\[\left \{\left \{y(x)\to e^{-\frac {i \sqrt {c} x}{\sqrt {a}}} x^{\frac {\sqrt {a^2-2 a (b+2 f)+b^2}+a-b}{2 a}} \left (c_1 U\left (\frac {a+\frac {i d \sqrt {a}}{\sqrt {c}}+\sqrt {a^2-2 (b+2 f) a+b^2}}{2 a},\frac {a+\sqrt {a^2-2 (b+2 f) a+b^2}}{a},\frac {2 i \sqrt {c} x}{\sqrt {a}}\right )+c_2 L_{-\frac {\sqrt {a^2-2 a (b+2 f)+b^2}+\frac {i \sqrt {a} d}{\sqrt {c}}+a}{2 a}}^{\frac {\sqrt {a^2-2 a (b+2 f)+b^2}}{a}}\left (\frac {2 i \sqrt {c} x}{\sqrt {a}}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.302 (sec), leaf count = 106
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {b}{2\,a}}} \left ( {{\sl M}_{{-{\frac {i}{2}}d{\frac {1}{\sqrt {c}}}{\frac {1}{\sqrt {a}}}},\,{\frac {1}{2\,a}\sqrt {{a}^{2}+ \left ( -2\,b-4\,f \right ) a+{b}^{2}}}}\left ({2\,ix\sqrt {c}{\frac {1}{\sqrt {a}}}}\right )}{\it \_C1}+{{\sl W}_{{-{\frac {i}{2}}d{\frac {1}{\sqrt {c}}}{\frac {1}{\sqrt {a}}}},\,{\frac {1}{2\,a}\sqrt {{a}^{2}+ \left ( -2\,b-4\,f \right ) a+{b}^{2}}}}\left ({2\,ix\sqrt {c}{\frac {1}{\sqrt {a}}}}\right )}{\it \_C2} \right ) \right \} \]