\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) }{x \left ( -1+F \left ( xy \left ( x \right ) \right ) y \left ( x \right ) \right ) }}=0} \]
Mathematica: cpu = 17.029162 (sec), leaf count = 74 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \frac {F'(K[1] K[2])}{F(K[1] K[2])^2} \, dK[1]-\frac {1}{K[2] F(x K[2])}+1\right ) \, dK[2]+\int _1^x -\frac {1}{K[1] F(y(x) K[1])} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.109 (sec), leaf count = 26 \[ \left \{ -y \left ( x \right ) +\int ^{xy \left ( x \right ) }\!{\frac {1 }{F \left ( {\it \_a} \right ) {\it \_a}}}{d{\it \_a}}-{\it \_C1}=0 \right \} \]