ABSTRACT
This study of “differential equations” begins with at least a few basic questions — questions that any thoughtful beginner should ask:
What are “differential equations”?
What can be done with them? Solve them? Just what is a “solution”, and how does one go about finding “solutions”?
and, of course,
What good are they anyway?
This chapter begins the study of differential equations by addressing these questions. The idea of a “differential equation” is clearly laid out, along with some of the ways of classifying the various differential equations. Just what is meant by a “solution to a differential equation” is developed and clarified with attention given to the difference between a “general solution” and a “particular solution”. In addition, the role of auxiliary conditions (such as “initial values”) in determining a desired particular solution to a differential equation is examined. Finally, enlightening applications are developed illustrating these concepts and the importance of differential equations in the sciences and engineering.
