Chapter 2.2, Problem 7E

Interpretation Introduction

Interpretation:

The equation ${\dot{\text{x}}\text{ = e}}^x\text{ - cos x}$ is to be analyzed graphically. Sketch the vector field on the real line, finding all fixed points, clarify their stability. If possible, the analytic solution for $\text{ x(t)}$ is to be obtained.

Concept Introduction:

Fixed points are the points where $\dot{\text{x}}\text{ = 0}$.

Stable points are points at which the local flow is toward them. They represent stable equilibria at which small disturbances damp out in time away from it.

Unstable points are points at which the local flow is away from them. They represent unstable equilibria.