\[ y'(x)=\frac {F\left (\frac {y(x)}{x}\right )+y(x)}{x-1} \] ✓ Mathematica : cpu = 0.174556 (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 = 0.025 (sec), leaf count = 29
\[y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} \right )+\ln \left (x -1\right )-\ln \relax (x )+c_{1}\right ) x\]