Chapter 2.2, Problem 9E

Interpretation Introduction

Interpretation:

An equation $\dot{\text{x}}\text{ = f(x)}$ is to be found whose solutions $\text{x(t)}$ are consistent with the given figure.

Concept Introduction:

Fixed points are the points where $\dot{\text{x}}\text{ = 0}$.

If $\text{x(t)}$ approaches asymptotically toward a point, then it is the stable point, and if $\text{x(t)}$ moves away from a point, then it is the unstable point.

The point where the flow is towards it is the stable point, and the point where the flow is away from it is called the unstable point.