\[ a x^2 y''(x)+b x y'(x)+y(x) \left (c x^2+d x+f\right )=0 \] ✓ Mathematica : cpu = 0.103436 (sec), leaf count = 310
DSolve[(f + d*x + c*x^2)*y[x] + b*x*Derivative[1][y][x] + a*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {HypergeometricU}\left (-\frac {-\sqrt {c} a-i d \sqrt {a}-\sqrt {c} \sqrt {a^2-2 b a-4 f a+b^2}}{2 a \sqrt {c}},\frac {\sqrt {a^2-2 b a-4 f a+b^2}}{a}+1,\frac {2 i \sqrt {c} x}{\sqrt {a}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {a^2-2 a b-4 a f+b^2}+a-b\right )-2 i \sqrt {a} \sqrt {c} x}{2 a}\right )+c_2 L_{\frac {-\sqrt {c} a-i d \sqrt {a}-\sqrt {c} \sqrt {a^2-2 b a-4 f a+b^2}}{2 a \sqrt {c}}}^{\frac {\sqrt {a^2-2 b a-4 f a+b^2}}{a}}\left (\frac {2 i \sqrt {c} x}{\sqrt {a}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {a^2-2 a b-4 a f+b^2}+a-b\right )-2 i \sqrt {a} \sqrt {c} x}{2 a}\right )\right \}\right \}\] ✓ Maple : cpu = 0.372 (sec), leaf count = 106
dsolve(a*x^2*diff(diff(y(x),x),x)+b*x*diff(y(x),x)+(c*x^2+d*x+f)*y(x)=0,y(x))
\[y \left (x \right ) = x^{-\frac {b}{2 a}} \left (\operatorname {WhittakerM}\left (-\frac {i d}{2 \sqrt {a}\, \sqrt {c}}, \frac {\sqrt {a^{2}+\left (-2 b -4 f \right ) a +b^{2}}}{2 a}, \frac {2 i \sqrt {c}\, x}{\sqrt {a}}\right ) c_{1}+\operatorname {WhittakerW}\left (-\frac {i d}{2 \sqrt {a}\, \sqrt {c}}, \frac {\sqrt {a^{2}+\left (-2 b -4 f \right ) a +b^{2}}}{2 a}, \frac {2 i \sqrt {c}\, x}{\sqrt {a}}\right ) c_{2}\right )\]