I was studying ODE (with a book by Sotomayor) and I got stuck with this one problem.
Let $$\frac{dx}{dt}=F \left(\frac{at + bx+c}{dt+ex+f} \right)\tag{$*$}$$
where $a,b,c,d,e,f$ is constants. If $ae=bd$, then find a change of variables such that transform $(*)$ into a separable variable equation (i.e. $\frac{dx}{dt}=F(t)H(x)$ or $\frac{dx}{dt}=G(t)F(x)$ ).
Any help would be appreciated!!