DIFFERENTIAL EQUATIONS with Boundary-Value Problems by Dennis G. Zill 7th Edition

Introduction

The words differential and equations certainly suggest solving some kind of
equation that contains derivatives y , y , . . . . Analogous to a course in algebra and
trigonometry, in which a good amount of time is spent solving equations such as
x2 5x 4 0 for the unknown number x, in this course one of our tasks will be
to solve differential equations such as y 2y y 0 for an unknown function
y (x).
The preceding paragraph tells something, but not the complete story, about the
course you are about to begin. As the course unfolds, you will see that there is more
to the study of differential equations than just mastering methods that someone has
devised to solve them.
But first things first. In order to read, study, and be conversant in a specialized
subject, you have to learn the terminology of that discipline. This is the thrust of the
first two sections of this chapter. In the last section we briefly examine the link
between differential equations and the real world. Practical questions such as How
fast does a disease spread? How fast does a population change? involve rates of
change or derivatives. As so the mathematical description—or mathematical
model—of experiments, observations, or theories may be a differential equation.