Chapter 6.6, Problem 2E

Interpretation Introduction

Interpretation:

To show that the system $\dot{\text{x}}\text{ = y , }\dot{\text{y}}\text{ = x cos y}$ is reversible and sketch the phase portraits.

Concept Introduction:

The system of the form $\dot{\text{x}}\text{ = f}\left(\text{x, y}\right)$ and $\dot{\text{y}}\text{ = g}\left(\text{x, y}\right)$ is said to be reversible when f is odd in y and g is even in y. Another way is $\text{f (x,-y) = - f(x, y) and g (x,-y) = g(x, y)}$.