Chapter 2.7, Problem 21P

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.

$y\text{'}=\epsilon y-\sigma y^3,\epsilon >0$ and $\sigma >0$. This equation occurs in the study of stability of fluid flow.

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.