\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{x-1} \left ( y \left ( x \right ) +F \left ( {\frac {y \left ( x \right ) }{x}} \right ) \right ) }=0} \]
Mathematica: cpu = 0.077010 (sec), leaf count = 36 \[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}} \frac {1}{F(K[1])+K[1]} \, dK[1]=c_1+\log (1-x)-\log (x),y(x)\right ] \]
Maple: cpu = 0.032 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) +{\it \_a} \right ) ^{-1}{d{\it \_a} }-\ln \left ( x \right ) +\ln \left ( x-1 \right ) +{\it \_C1} \right ) x \right \} \]