Chapter 3.1, Problem 29E

(a)

To determine

Find the equilibrium solutions of $\frac{dy}{dt}=-r\left(1-\frac{y}{A}\right)y$ and sketch the phase line.

(b)

To determine

To describe: The difference of the differential equation $\frac{dy}{dt}=-r\left(1-\frac{y}{A}\right)y$ and the logistic equation.

(c)

To determine

The value of ${\lim }_{t\to \infty }y\left(t\right)$, where $A=2$ and $y\left(0\right)=1$.

(d)

To determine

The value of ${\lim }_{t\to \infty }y\left(t\right)$, where $A=2$ and $y\left(0\right)=3$.