In this chapter we’re going to take a look at higher order
differential equations. This chapter
will actually contain more than most text books tend to have when they discuss
higher order differential equations.

We will definitely cover the same material that most text
books do here. However, in all the
previous chapters all of our examples were 2^{nd} order differential
equations or 2 x 2 systems of differential equations. So, in this chapter we’re also going to do a
couple of examples here dealing with 3^{rd} order or higher
differential equations with Laplace transforms and series as well as a
discussion of some larger systems of differential equations.

Here is a brief listing of the topics in this chapter.

**Basic Concepts for ***n*^{th} Order Linear Equations We’ll start the chapter off with a quick look
at some of the basic ideas behind solving higher order linear differential
equations.

**Homogeneous Linear Higher Order Differential
Equations**** ** In this section we’ll take a look at extending
the ideas behind solving 2^{nd} order differential equations to higher
order.

** **

**Undetermined Coefficients** Here we’ll look at undetermined coefficients
for higher order differential equations.

**Variation of Parameters** We’ll look at variation of parameters for
higher order differential equations in this section.

**Laplace Transforms** In this section we’re just going to work an
example of using Laplace transforms to solve a differential equation on a 3^{rd}
order differential equation just so say that we looked at one with order higher
than 2^{nd}.

**Systems of Differential Equations** Here we’ll take a quick look at extending the
ideas we discussed when solving 2 x 2 systems of differential equations to
systems of size 3 x 3.

**Series Solutions** This section serves the same purpose as the
Laplace Transform section. It is just
here so we can say we’ve worked an example using series solutions for a
differential equations of order higher than 2^{nd}.