Chapter 2.7, Problem 20P

In each of Problems $13$ through $22$:

Write the Bernoulli equation in the proper form (19).

Solve the equation.

Use a computer to draw several integral curves.

$y\text{'}=ry-k{y}^2,r>0$ and $k>0$. This equation is important in population dynamics and is discussed in detail in Section $2.5$.

Bernoulli Differential Equation. Adifferential equation of the form

$\frac{dy}{dt}+q\left(t\right)y=r\left(t\right)y^n$, (19)

Where $n$ is any real number, is called a Bernoulli equation.