In 25–28, find at least the first four nonzero terms in a

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

ISBN: 9780321747730 43

Solution for problem 25E Chapter 8.3

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition

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Problem 25E

In Problems 25–28, find at least the first four nonzero terms in a power series expansion about $x=0$ for the solution to the given initial value problem.

$w^{\prime \prime}+3 x w^{\prime}-w=0$

$w(0)=2, w^{\prime}(0)=0$

Equation Transcription:

$x=0$

$w''+3xw'-w=0$

$w(0)=2,\ w'(0)=0$

Text Transcription:

x=0

w''+3xw'-w=0

w(0)=2, w'(0)=0

Step-by-Step Solution:

Step 1 of 6

We know that

Therefore, it has no singular points which means that is an ordinary point.

Consider a solution of the form:

To substitute in the given equation, we need to find its first and second derivative, with respect to .

Step 2 of 6

Chapter 8.3, Problem 25E is Solved

Step 3 of 6

Textbook: Fundamentals of Differential Equations

Edition: 8

Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider

ISBN: 9780321747730

This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. The full step-by-step solution to problem: 25E from chapter: 8.3 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Since the solution to 25E from 8.3 chapter was answered, more than 382 students have viewed the full step-by-step answer. The answer to “?In 25–28, find at least the first four nonzero terms in a power series expansion about $x=0$ for the solution to the given initial value problem.$w^{\prime \prime}+3 x w^{\prime}-w=0$$w(0)=2, w^{\prime}(0)=0$Equation Transcription:Text Transcription:x=0w''+3xw'-w=0w(0)=2, w'(0)=0” is broken down into a number of easy to follow steps, and 33 words. This full solution covers the following key subjects: Expansion, Find, given, initial, least. This expansive textbook survival guide covers 67 chapters, and 2118 solutions.