Advanced Engineering Mathematics, 7th Edition

3.1 Theory of Linear Equations

INTRODUCTION

We turn now to differential equations of order two or higher. In this section we will examine some of the underlying theory of linear DEs. Then in the five sections that follow we learn how to solve linear higher-order differential equations.

3.1.1. Initial-Value and Boundary-Value Problems

Initial-Value Problem

In Section 1.2 we defined an initial-value problem for a general nth-order differential equation. For a linear differential equation, an nth-order initial-value problem (IVP) is

(1)

Recall ...