Table of Contents#### Download Safari Books Online apps: Apple iOS | Android | BlackBerry

## 5.1 Power Series Method

Entire Site

Free Trial

Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.

The **power series method** is the standard method for solving linear ODEs with ** variable** coefficients. It gives solutions in the form of power series. These series can be used for computing values, graphing curves, proving formulas, and exploring properties of solutions, as we shall see. In this section we begin by explaining the idea of the power series method.

From calculus we remember that a **power series** (in powers of *x* − *x*_{0}) is an infinite series of the form

Here, *x* is a variable. *a*_{0}, *a*_{1}, *a*_{2}, … are constants, called the **coefficients** of the series. *x*_{0} is a constant, called the **center** of the series. In particular, if *x*_{0} = 0, we obtain a **power series in powers of x**

We shall assume that all variables and constants are real.