\[ y(x) \left (a x^2+b x+c+x f'(x)+f(x)^2-f(x)\right )+2 x f(x) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.104074 (sec), leaf count = 218
DSolve[y[x]*(c + b*x + a*x^2 - f[x] + f[x]^2 + x*Derivative[1][f][x]) + 2*x*f[x]*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 U\left (-\frac {-i b-\sqrt {a}-\sqrt {a} \sqrt {1-4 c}}{2 \sqrt {a}},\sqrt {1-4 c}+1,2 i \sqrt {a} x\right ) \exp \left (\int _1^x\frac {-2 f(K[1])-2 i \sqrt {a} K[1]+\sqrt {1-4 c}+1}{2 K[1]}dK[1]\right )+c_2 L_{\frac {-i b-\sqrt {a}-\sqrt {a} \sqrt {1-4 c}}{2 \sqrt {a}}}^{\sqrt {1-4 c}}\left (2 i \sqrt {a} x\right ) \exp \left (\int _1^x\frac {-2 f(K[1])-2 i \sqrt {a} K[1]+\sqrt {1-4 c}+1}{2 K[1]}dK[1]\right )\right \}\right \}\] ✓ Maple : cpu = 0.092 (sec), leaf count = 69
dsolve(x^2*diff(diff(y(x),x),x)+2*x*f(x)*diff(y(x),x)+(x*diff(f(x),x)+f(x)^2-f(x)+a*x^2+b*x+c)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\left (\int \frac {f \left (x \right )}{x}d x \right )} \left (c_{1} \WhittakerM \left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right )+c_{2} \WhittakerW \left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right )\right )\]