Given the autonomous differential equation:

$\frac{dy}{dt}=0\mathrm{.}2y(5-y)(y-2)$

a$.$ Find the equilibrium points. Classify each of them as stable, unstable, or semi$-$stable.

b$.$ Sketch a graph of $y$ vs $t$ in the yt$-$plane. Draw several solution curves.

c$.$ Suppose that this equation models a population of rats $($given in thousands of rats$)$ for a particular region. Explain the meaning of $5$ and $2$ in the model. What do they represent?