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.