Chapter 6.5, Problem 3E

Interpretation Introduction

Interpretation:

The conserved quantity for the system ${\ddot{\text{x}}\text{ = a - e}}^x$ is to be found and itsphase portraitfor $\text{ a < 0, a = 0, and a > 0}$ is to be sketched.

Concept Introduction:

The trajectories of the dynamic system are called phase portrait.

Phase portrait gives the qualitative behavior of the solutions of a differential equation.

The conserved quantity of the system is energy.