\[ y'(x)=\frac {F(x (y(x)+x))-y(x)-2 x}{x} \] ✓ Mathematica : cpu = 50.1182 (sec), leaf count = 116
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {K[1] (2 K[1]+K[2]) F'(K[1] (K[1]+K[2]))-F(K[1] (K[1]+K[2]))}{F(K[1] (K[1]+K[2]))^2} \, dK[1]-\frac {x}{F(x (K[2]+x))}\right ) \, dK[2]+\int _1^x \frac {F(K[1] (K[1]+y(x)))-2 K[1]-y(x)}{F(K[1] (K[1]+y(x)))} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.09 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {-{x}^{2}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{x}} \right \} \]