Calculus II Workbook For Dummies

Chapter 14

Differential Equations

IN THIS CHAPTER

Understanding how differential equations arise and how to begin thinking about them

Solving separable differential equations

Differential equations (DEs for short) are complicated-looking equations that arise when you combine functions and their derivatives. DEs are useful for modeling a wide variety of phenomena in both physical sciences (such as physics, chemistry, and biology) and social sciences (such as economics and sociology). And although some DEs are extremely difficult to solve, others yield readily to a few methods that you’re already well prepared to learn in a Calculus II class.

In this chapter, I show you how the most basic DE arises naturally whenever you find a derivative, and how it can be solved by integration. After that, I show you how even slightly more complicated DEs get a lot trickier to solve. I also provide you with a way to begin building DEs and then testing solutions to them.

This work provides a basis for solving separable equations, which are the first type of DE most students work with because they’re the easiest to solve. Solving separable equations leans heavily on integration, which is why some Calculus II courses have begun to include a unit on this basic type of DE.

Understanding Differential ...