Advanced Engineering Mathematics, 7th Edition

2.3 Linear Equations

INTRODUCTION

We continue our search for solutions of first-order DEs by next examining linear equations. Linear differential equations are an especially “friendly” family of differential equations in that, given a linear equation, whether first-order or a higher-order kin, there is always a good possibility that we can find some sort of solution of the equation that we can look at.

A Definition

The form of a linear first-order DE was given in (7) of Section 1.1. This form, the case when n = 1 in (6) of that section, is reproduced here for convenience.

DEFINITION 2.3.1 Linear Equation

A first-order differential equation ...