If you consider the classic differential equation used in textbooks to model animal population growth and forget adding in the carrying capacity terms:
$dP/dt$ = rP
It would seem that the above DE would benefit from some variable rate r instead of some fixed rate r in order to achieve a more accurate model.
I tried googling around for this and I'm guessing I simply wasn't using the best keywords. I'm wondering if someone could give an example of a DE where a variable rate r is used and how one usually solves such an equation.