Chapter 7.6, Problem 14E

Interpretation Introduction

Interpretation:

• (a) To derive the average equation

• (b) To solve the averaged equation and find an approximate formula for the given differential equation for the given initial conditions.

• (c) To solve the plot differential equation by solving it numerically and to compare it with (b)

Concept Introduction:

• ➢ Fixed point of a differential equation is a point where $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$

• ➢ Nullclines are the curves where either $\dot{\text{x}}=0\text{ or }\dot{\text{y}}\text{ = 0}$;they show whether the flow is completely vertical or horizontal.

• ➢ Phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about evolution of the system, its fixed points, whether they will attract or repel the flow, etc.