\[ y'(x)=\frac {F(x (x y(x)-1))-2 x^3 y(x)+x^2}{x^4} \] ✓ Mathematica : cpu = 0.469631 (sec), leaf count = 177
DSolve[Derivative[1][y][x] == (x^2 + F[x*(-1 + x*y[x])] - 2*x^3*y[x])/x^4,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x^2+F(x (x K[2]-1)) \int _1^x\left (\frac {2 K[2] F'(K[1] (K[1] K[2]-1)) K[1]^3}{F(K[1] (K[1] K[2]-1))^2}-\frac {F'(K[1] (K[1] K[2]-1)) K[1]^2}{F(K[1] (K[1] K[2]-1))^2}-\frac {2 K[1]}{F(K[1] (K[1] K[2]-1))}\right )dK[1]}{F(x (x K[2]-1))}dK[2]+\int _1^x\left (-\frac {2 K[1] y(x)}{F(K[1] (K[1] y(x)-1))}+\frac {1}{F(K[1] (K[1] y(x)-1))}+\frac {1}{K[1]^2}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.09 (sec), leaf count = 26
dsolve(diff(y(x),x) = -1/x^4*(-x^2+2*x^3*y(x)-F((x*y(x)-1)*x)),y(x))
\[y \left (x \right ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right ) x +x c_{1}+1\right )+x}{x^{2}}\]