In this chapter we will finally be looking at nonconstant
coefficient differential equations.
While we won’t cover all possibilities in this chapter we will be
looking at two of the more common methods for dealing with this kind of differential
equation.
The first method that we’ll be taking a look at, series
solutions, will actually find a series representation for the solution instead
of the solution itself. You first saw
something like this when you looked at Taylor
series in your Calculus class. As we
will see however, these won’t work for every differential equation.
The second method that we’ll look at will only work for a
special class of differential equations.
This special case will cover some of the cases in which series solutions
can’t be used.
Here is a brief listing of the topics in this chapter.
Review : Power
Series A brief review of some of the basics of power
series.
Review : Taylor Series A reminder on how to construct the Taylor series for a
function.
Series Solutions In this section we will construct a series
solution for a differential equation about an ordinary point.
Euler Equations We will look at solutions to Euler’s
differential equation in this section.