1. The problem is to provide an example of a logistic differential equation. 2. A logistic differential equation models population growth with a carrying capacity, limiting the growth as the population approaches this capacity. 3. The general form of the logistic differential equation is: $$\frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right)$$ where: - $P$ is the population at time $t$, - $r$ is the intrinsic growth rate, - $K$ is the carrying capacity of the environment. 4. This equation states that the rate of change of the population is proportional to both the current population and the fraction of the carrying capacity remaining. 5. For example, if $r=0.5$ and $K=1000$, the logistic differential equation becomes: $$\frac{dP}{dt} = 0.5P\left(1 - \frac{P}{1000}\right)$$ This means the population grows quickly when small, but growth slows as $P$ approaches 1000. 6. This model is widely used in biology, ecology, and other fields to describe constrained growth.