\[ \boxed { a{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +bx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( c{x}^{2}+dx+f \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.287037 (sec), leaf count = 310 \[ \left \{\left \{y(x)\to c_1 U\left (-\frac {-\sqrt {c} a-i d \sqrt {a}-\sqrt {c} \sqrt {a^2-2 b a-4 f a+b^2}}{2 a \sqrt {c}},\frac {\sqrt {a^2-2 b a-4 f a+b^2}}{a}+1,\frac {2 i \sqrt {c} x}{\sqrt {a}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {a^2-2 a b-4 a f+b^2}+a-b\right )-2 i \sqrt {a} \sqrt {c} x}{2 a}\right )+c_2 L_{\frac {-\sqrt {c} \sqrt {a^2-2 a b-4 a f+b^2}+a \left (-\sqrt {c}\right )-i \sqrt {a} d}{2 a \sqrt {c}}}^{\frac {\sqrt {a^2-2 a b-4 a f+b^2}}{a}}\left (\frac {2 i \sqrt {c} x}{\sqrt {a}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {a^2-2 a b-4 a f+b^2}+a-b\right )-2 i \sqrt {a} \sqrt {c} x}{2 a}\right )\right \}\right \} \]
Maple: cpu = 0.218 (sec), leaf count = 113 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {b}{2\,a}}}{ {\sl M}_{{-{\frac {i}{2}}d{\frac {1}{\sqrt {c}}}{\frac {1}{\sqrt {a}}} },\,{\frac {1}{2\,a}\sqrt {{a}^{2}+ \left ( -2\,b-4\,f \right ) a+{b}^{2 }}}}\left ({2\,ix\sqrt {c}{\frac {1}{\sqrt {a}}}}\right )}+{\it \_C2}\,{ x}^{-{\frac {b}{2\,a}}}{{\sl W}_{{-{\frac {i}{2}}d{\frac {1}{\sqrt {c} }}{\frac {1}{\sqrt {a}}}},\,{\frac {1}{2\,a}\sqrt {{a}^{2}+ \left ( -2 \,b-4\,f \right ) a+{b}^{2}}}}\left ({2\,ix\sqrt {c}{\frac {1}{\sqrt {a} }}}\right )} \right \} \]