Chapter 7.2, Problem 7E

Interpretation Introduction

Interpretation:

To show that $\frac{\partial \text{f}}{\partial \text{y}}\text{ = }\frac{\partial \text{g}}{\partial \text{x}}$ for the system $\dot{\text{x}}\text{ = y + 2xy}$, ${\dot{\text{y}}\text{ = x + x}}^{\text{2}}{\text{- y}}^{\text{2}}$. To find $\text{V}$. To sketch the phase portrait.

Concept Introduction:

$\text{V}$ is a function such that $\frac{\text{-}\partial \text{V}}{\partial \text{x}}\text{ = }\dot{\text{x}}$ and $\frac{\text{-}\partial \text{V}}{\partial \text{y}}\text{ = }\dot{\text{y}}$