Chapter 6.6, Problem 10E

Interpretation Introduction

Interpretation:

To check the origin is center for the f the nonlinear system ${\dot{\text{x}}\text{ = -y - x}}^{\text{2}}\text{, }\dot{\text{y}}\text{ = x}$.

Concept Introduction:

Determine fixed points for the given system.

Find the determinant for the given point to determine the center of the system.

Use even / odd property to determine the system is reversible or not.