\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x+F \left ( - \left ( x-y \left ( x \right ) \right ) \left ( y \left ( x \right ) +x \right ) \right ) }{y \left ( x \right ) }}=0} \]
Mathematica: cpu = 31.940556 (sec), leaf count = 106 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x -\frac {2 K[1] K[2] F'((K[2]-K[1]) (K[1]+K[2]))}{F((K[2]-K[1]) (K[1]+K[2]))^2} \, dK[1]-\frac {K[2]}{F((K[2]-x) (K[2]+x))}\right ) \, dK[2]+\int _1^x \left (\frac {K[1]}{F((y(x)-K[1]) (K[1]+y(x)))}+1\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.109 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+{\it RootOf} \left ( -2\,x+ \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d {\it \_a}}+2\,{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {{x}^{2} +{\it RootOf} \left ( -2\,x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) } \right \} \]