Advanced Engineering Mathematics, 7th Edition

3.10 Green’s Functions

INTRODUCTION

We have seen in Section 3.8 that the linear second-order differential equation

(1)

plays an important role in applications. In the mathematical analysis of physical systems it is often desirable to express the response or output y(x) of (1) subject to either initial conditions or boundary conditions directly in terms of the forcing function or input g(x). In this manner the response of the system can quickly be analyzed for different forcing functions.

To see how this is done we start by examining solutions of initial-value problems in which the DE (1) has been put into the standard form

(2)

by dividing ...