We consider the utilization of power series to determine solutions to more general differential equations.

Series Solutions Near an Ordinary Point II

In this section we continue to find series solutions of initial value problems

where , and are polynomials and , so is an ordinary point of (eq:7.3.1). However, here we consider cases where the differential equation in (eq:7.3.1) is not of the form so Theorem thmtype:7.2.2 does not apply, and the computation of the coefficients is more complicated. For the equations considered here it’s difficult or impossible to obtain an explicit formula for in terms of . Nevertheless, we can calculate as many coefficients as we wish. The next three examples illustrate this.

Text Source

Trench, William F., ”Elementary Differential Equations” (2013). Faculty Authored and Edited Books & CDs. 8. (CC-BY-NC-SA)