Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time $x(t)\to \pm \infty$, where $\text{r > 0}$

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation ${\dot{\text{x}}\text{ = rx+x}}^{\text{3}}$ where $\text{r > 0}$, is found out.

The existence and uniqueness theorem says that, ‘$\text{f(x)}$, and $\text{f'(x)}$ are continuous on an open interval R of the x-axis, and suppose that ${\text{ x}}_0$ is a point in R. Then the initial value problem has a solution $\text{x(t)}$ on some time interval $\text{(-t,t)}$ about $\text{t = 0}$, and the solution is unique’.