\[ y'(x)=\frac {F(x (y(x)+x))-y(x)-2 x}{x} \] ✓ Mathematica : cpu = 48.1036 (sec), leaf count = 188
\[\text {Solve}\left [\int _1^{y(x)} -\frac {F(x (K[2]+x)) \int _1^x \left (\frac {2 K[1]^2 F'(K[1] (K[1]+K[2]))}{F(K[1] (K[1]+K[2]))^2}+\frac {K[1] (K[2]-F(K[1] (K[1]+K[2]))) F'(K[1] (K[1]+K[2]))}{F(K[1] (K[1]+K[2]))^2}-\frac {1-K[1] F'(K[1] (K[1]+K[2]))}{F(K[1] (K[1]+K[2]))}\right ) \, dK[1]+x}{F(x (K[2]+x))} \, dK[2]+\int _1^x \left (-\frac {2 K[1]}{F(K[1] (K[1]+y(x)))}-\frac {y(x)-F(K[1] (K[1]+y(x)))}{F(K[1] (K[1]+y(x)))}\right ) \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.092 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {-{x}^{2}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{x}} \right \} \]