\[ y'(x)=\frac {F(x (x y(x)-1))-2 x^3 y(x)+x^2}{x^4} \] ✓ Mathematica : cpu = 0.491442 (sec), leaf count = 177
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x^2+F(x (x K[2]-1)) \int _1^x\left (\frac {2 K[2] F'(K[1] (K[1] K[2]-1)) K[1]^3}{F(K[1] (K[1] K[2]-1))^2}-\frac {F'(K[1] (K[1] K[2]-1)) K[1]^2}{F(K[1] (K[1] K[2]-1))^2}-\frac {2 K[1]}{F(K[1] (K[1] K[2]-1))}\right )dK[1]}{F(x (x K[2]-1))}dK[2]+\int _1^x\left (-\frac {2 K[1] y(x)}{F(K[1] (K[1] y(x)-1))}+\frac {1}{F(K[1] (K[1] y(x)-1))}+\frac {1}{K[1]^2}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.143 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}x+{\it \_C1}\,x+1 \right ) +x}{{x}^{2}}} \right \} \]