ODE No. 598

$$y^{\prime }(x)=\frac{F\left(\frac{y(x)}{x}\right)+y(x)}{x-1}$$ ✓ Mathematica : cpu = 0.174556 (sec), leaf count = 37

DSolve[Derivative[1][y][x] == (F[y[x]/x] + y[x])/(-1 + x),y[x],x]
 

$$\text{Solve}[{\int }_1^{\frac{y(x)}{x}}\frac{1}{F(K[1])+K[1]}dK[1]=\log (1-x)-\log (x)+c_1,y(x)]$$ ✓ Maple : cpu = 0.025 (sec), leaf count = 29

dsolve(diff(y(x),x) = (y(x)+F(y(x)/x))/(x-1),y(x))
 

$$y\left(x\right)=\mathrm{RootOf}(-\left({\int }_{}^{\mathit{\text{\_Z}}}\frac{1}{F\left(\mathit{\text{\_a}}\right)+\mathit{\text{\_a}}}d\mathit{\text{\_a}}\right)+\ln (x-1)-\ln \left(x\right)+c_1)x$$