Differential Equations Workbook For Dummies®

Chapter 2. Surveying Separable First Order Differential Equations

In This Chapter

• Diving into separable differential equations

• Knowing how to obtain implicit solutions

• Practicing the y = vx trick for separating differential equations

• Solving separable first order differential equations with initial conditions

Welcome to separable differential equations! You know 'em; you may even love 'em. After all, they let you separate out the variables so only one variable appears on each side of the equal sign. What's not to love about that?

In this chapter, you're not going to limit yourself to linear differential equations (like those covered in Chapter 1). That is, you may see something like this:

But because the equations in this chapter are still considered first order, you can expect to see something along these lines:

To restrict the form of this differential equation even more, say that M(x, y) is really just a function of x — that is, M(x). Similarly, say that N(x, y) is really just a function of y — that is, N(y). Combined, that gives you

This differential equation is considered separable, because it can be written in a form where all terms in x are on one side of the equal sign ...