Chapter 2.2, Problem 2E

Interpretation Introduction

Interpretation:

Analyze ${\dot{\text{x}}\text{=1- x}}^{\text{14}}$ graphically. Plot the vector field on the real line, finding all fixed points, classify their stability and sketch the graph of $\text{x}\left(\text{t}\right)$ for different initial conditions.

Concept Introduction:

For a flow, equation is represented by $\dot{\text{x}}\text{=f}\left(\text{x}\right)$

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

When vector field for flow is represented on the real line, among these fixed points, the points where the flow is towards them are called stable points, and the points where the flow is away from them are called unstable points.