Chapter 17, Problem 5RCC

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# How do you use power series to solve a differential equation?

To determine

To explain: The steps to use of power series to solve a differential equation.

Explanation

Suppose the differential equation is as follows.

b0(x)dnydxn+b1(x)dnâˆ’1ydxnâˆ’1+...+bnâˆ’1(x)dydx+bn(x)y=G(x) (1)

The following steps are used to solve a differential equation.

• Consider a solution of the form as follows.

y=a0+a1x+a2x2+a3x3+... (2)

Here,

a0 , a1 ,â€¦ anâˆ’1 are arbitrary constants.

• Substitute the equation (2) in equation (1),

A0(a0,a1,a3,...)+A1(a0,a1,a3,

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