Chapter 7.2, Problem 3E

Interpretation Introduction

Interpretation:

To plot the phase portrait for gradient system.

Concept Introduction:

Gradient systems: If the system can be written in the form $\dot{\text{x}}=-\nabla \text{V}$, for continuously differentiable, the single-valued scalar function $\text{V(x)}$ then the system is called a gradient system with a potential function V.

$\nabla V$ can be written as

$\nabla \text{V=}\frac{\delta V}{\delta \text{x}}+\frac{\delta V}{\delta \text{y}}$