\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-2\,{x}^{2}+x+F \left ( y \left ( x \right ) +{x}^{2}-x \right ) }{x}}=0} \]
Mathematica: cpu = 49.763319 (sec), leaf count = 153 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {F\left (K[2]+x^2-x\right ) \int _1^x \left (\frac {2 K[1] F'\left (K[1]^2-K[1]+K[2]\right )}{F\left (K[1]^2-K[1]+K[2]\right )^2}-\frac {F'\left (K[1]^2-K[1]+K[2]\right )}{F\left (K[1]^2-K[1]+K[2]\right )^2}\right ) \, dK[1]+1}{F\left (K[2]+x^2-x\right )} \, dK[2]+\int _1^x \left (-\frac {2 K[1]}{F\left (K[1]^2-K[1]+y(x)\right )}+\frac {1}{F\left (K[1]^2-K[1]+y(x)\right )}+\frac {1}{K[1]}\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.093 (sec), leaf count = 26 \[ \left \{ y \left ( x \right ) =-{x}^{2}+{\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) +x \right \} \]