\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,xf \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( x{\frac {\rm d}{{\rm d}x}}f \left ( x \right ) + \left ( f \left ( x \right ) \right ) ^{2}-f \left ( x \right ) +a{x}^{2}+bx+c \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 23.116936 (sec), leaf count = 216 \[ \left \{\left \{y(x)\to c_1 U\left (-\frac {-i b-\sqrt {a}-\sqrt {a} \sqrt {1-4 c}}{2 \sqrt {a}},\sqrt {1-4 c}+1,2 i \sqrt {a} x\right ) \exp \left (\int _1^x \frac {-2 i \sqrt {a} K[1]-2 f(K[1])+\sqrt {1-4 c}+1}{2 K[1]} \, dK[1]\right )+c_2 L_{\frac {-\sqrt {a} \sqrt {1-4 c}-\sqrt {a}-i b}{2 \sqrt {a}}}^{\sqrt {1-4 c}}\left (2 i \sqrt {a} x\right ) \exp \left (\int _1^x \frac {-2 i \sqrt {a} K[1]-2 f(K[1])+\sqrt {1-4 c}+1}{2 K[1]} \, dK[1]\right )\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 79 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}_{{-{\frac {i}{2}}b{ \frac {1}{\sqrt {a}}}},\,{\frac {1}{2}\sqrt {1-4\,c}}}\left (2\,i\sqrt {a}x\right )}{{\rm e}^{-\int \!{\frac {f \left ( x \right ) }{x}} \,{\rm d}x}}+{\it \_C2}\,{{\sl W}_{{-{\frac {i}{2}}b{\frac {1}{\sqrt { a}}}},\,{\frac {1}{2}\sqrt {1-4\,c}}}\left (2\,i\sqrt {a}x\right )}{ {\rm e}^{-\int \!{\frac {f \left ( x \right ) }{x}}\,{\rm d}x}} \right \} \]