Solution: First Order Equations. The series methods discussed in this section are

Chapter 5, Problem 18

(choose chapter or problem)

First Order Equations. The series methods discussed in this section are directly applicableto the first order linear differential equation P(x)y + Q(x)y = 0 at a point x0, if the functionp = Q/P has a Taylor series expansion about that point. Such a point is called an ordinarypoint, and further, the radius of convergence of the series y = n=0an(x x0)n is at least as largeas the radius of convergence of the series for Q/P. In each of 16 through 21, solve thegiven differential equation by a series in powers of x and verify that a0 is arbitrary in each case. 20 and 21 involve nonhomogeneous differential equations to which series methodscan be easily extended.Where possible, compare the series solution with the solution obtainedby using the methods of Chapter 2.y = ex2y, three terms only