\[ y'(x)=\frac {F\left (\frac {y(x)}{x}\right )+y(x)}{x-1} \] ✓ Mathematica : cpu = 0.162064 (sec), leaf count = 37
\[\text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{F(K[1])+K[1]}dK[1]=\log (1-x)-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.086 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) +{\it \_a} \right ) ^{-1}{d{\it \_a}}+\ln \left ( x-1 \right ) -\ln \left ( x \right ) +{\it \_C1} \right ) x \right \} \]