Chapter 10.1, Problem 35E

(a)

To determine

The solution for the logistic differential equation, $\frac{dy}{dt}=k\left(1-\frac{y}{N}\right)y$ such that $\frac{1}{y}+\frac{1}{N-y}=\frac{N}{\left(N-y\right)y}$.

(b)

To determine

To verify: The relation $b=\frac{\left(N-y_0\right)}{y_0}$ such that $0<y<N$ where, $y_0$ is the initial population.

(c)

To determine

To verify: The relation $b=\frac{\left(y_0-N\right)}{y_0}$ such that $0<N<y$ where, $y_0$ is the initial population.