\[ y'(x)=\frac {F\left (\frac {y(x)}{x}\right )+y(x)}{x-1} \] ✓ Mathematica : cpu = 0.174556 (sec), leaf count = 37
DSolve[Derivative[1][y][x] == (F[y[x]/x] + y[x])/(-1 + x),y[x],x]
\[\text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{F(K[1])+K[1]}dK[1]=\log (1-x)-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.025 (sec), leaf count = 29
dsolve(diff(y(x),x) = (y(x)+F(y(x)/x))/(x-1),y(x))
\[y \left (x \right ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} \right )+\ln \left (x -1\right )-\ln \left (x \right )+c_{1}\right ) x\]