First Order Equations. The series methods discussed in this section are
directly applicable to the first order linear differential equation at a point , if the function has a
Taylor series expansion about that point. Such a point is called an ordinary
point, and further, the radius of convergence of the series
is at least as large as
the radius of convergence of the series for In each of Problems 16
through 21 solve the given differential equation by a series in powers of
and verify that is arbitrary in each case. Problems 20 and 21 involve
nonhomogeneous differential equations to which series methods can be easily
extended. Where possible, compare the series solution with the solution
obtained by using the methods of Chapter 2 .