\[ y'(x)=\frac {F\left (\frac {y(x)}{x}\right )+y(x)}{x-1} \] ✓ Mathematica : cpu = 0.189332 (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 = 0.02 (sec), leaf count = 29
\[\left \{y \left (x \right ) = x \RootOf \left (c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} +F \left (\textit {\_a} \right )}d \textit {\_a} \right )-\ln \left (x \right )+\ln \left (x -1\right )\right )\right \}\]