\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-2\,x-y \left ( x \right ) +F \left ( x \left ( y \left ( x \right ) +x \right ) \right ) }{x}}=0} \]
Mathematica: cpu = 39.069461 (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 = 0.078 (sec), leaf count = 28 \[ \left \{ y \left ( x \right ) ={\frac {-{x}^{2}+{\it RootOf} \left ( -x+ \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d {\it \_a}}+{\it \_C1} \right ) }{x}} \right \} \]