\[ y'(x)=\frac {F\left (x^2+y(x)-x\right )-2 x^2+x}{x} \] ✓ Mathematica : cpu = 0.263732 (sec), leaf count = 156
DSolve[Derivative[1][y][x] == (x - 2*x^2 + F[-x + x^2 + y[x]])/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (x^2-x+K[2]\right ) \int _1^x\left (\frac {2 K[1] F'\left (K[1]^2-K[1]+K[2]\right )}{F\left (K[1]^2-K[1]+K[2]\right )^2}-\frac {F'\left (K[1]^2-K[1]+K[2]\right )}{F\left (K[1]^2-K[1]+K[2]\right )^2}\right )dK[1]+1}{F\left (x^2-x+K[2]\right )}dK[2]+\int _1^x\left (-\frac {2 K[1]}{F\left (K[1]^2-K[1]+y(x)\right )}+\frac {1}{F\left (K[1]^2-K[1]+y(x)\right )}+\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.092 (sec), leaf count = 26
dsolve(diff(y(x),x) = (-2*x^2+x+F(y(x)+x^2-x))/x,y(x))
\[y \left (x \right ) = -x^{2}+\operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right )+x\]