Chapter 1.2, Problem 21P

In each of problems $20$ through $23$ draw a direction field for the given differential equation. Based on the direction field, determine the behaviour of $y$ as $t\to \infty$. If this behaviour depends on the initial value of $y$ at $t=0$, describe the dependency. Note that in these problems the equations are not of the form $y\text{'}=ay+b$, and the behaviour of their solutions is somewhat more complicated than the solutions shown in figures $\mathrm{1.2.6}$ and $\mathrm{1.2.7}$.

$y\text{'}=-y(5-y)$