I remember that I have seen somewhere that the simplest mathematical model of population growth $$ \frac{{\rm d}P}{{\rm d}t}=kP $$ [where $P$ is the population at time $t$, ${\rm d}P/{\rm d}t$ is the rate of population and $k$ is a positive constant], can be solved without separating the variables in the differential equation. Unfortunately, I can recall neither the solution, nor the source.
For instance, say, we are given that the population has doubled in 6 years. How long it will take to triple? [Solving the problem with separation of variables, integration and using the condition gives $t=6\frac{\ln 3}{\ln 2}\approx 9.5$ years.]