Chapter 2.2, Problem 8E

Interpretation Introduction

Interpretation:

The equation consistent with the given phase portrait is to be determined.

Concept Introduction:

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

If the flow is towards the right, $\dot{\text{x}}\text{ > 0}$, and if it is towards left $\dot{\text{x}}\text{ < 0}$, $\dot{\text{x}}\text{ = 0}$ represents no flow.

Stable points are points at which the local flow is toward them.

Unstable points are points at which the local flow is away from them.

Semistable points are the points at which the local flow is towards them as well as away from them.