\[ y'(x)=\frac {F(x (y(x)+x))-y(x)-2 x}{x} \] ✓ Mathematica : cpu = 0.270072 (sec), leaf count = 191
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x+F(x (x+K[2])) \int _1^x\left (\frac {2 F'(K[1] (K[1]+K[2])) K[1]^2}{F(K[1] (K[1]+K[2]))^2}+\frac {(K[2]-F(K[1] (K[1]+K[2]))) F'(K[1] (K[1]+K[2])) K[1]}{F(K[1] (K[1]+K[2]))^2}-\frac {1-K[1] F'(K[1] (K[1]+K[2]))}{F(K[1] (K[1]+K[2]))}\right )dK[1]}{F(x (x+K[2]))}dK[2]+\int _1^x\left (-\frac {2 K[1]}{F(K[1] (K[1]+y(x)))}-\frac {y(x)-F(K[1] (K[1]+y(x)))}{F(K[1] (K[1]+y(x)))}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.14 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {-{x}^{2}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{x}} \right \} \]