In 13 and 14 verify by direct substitution that the given

Chapter 6, Problem 33E

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QUESTION:

In Problems 31–34 verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power \(x^{2 n+1} \text { let } k=n+1\).]

\(y=\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} x^{n}, \quad(x+1) y^{\prime \prime}+y^{\prime}=0\)

Text Transcription:

x^2n+1letk=n+1

y=sum_n=1^inftyfrac(-1)^n+1nx^n,(x+1)y^prime\prime+y^prime}=0

Questions & Answers

QUESTION:

In Problems 31–34 verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power \(x^{2 n+1} \text { let } k=n+1\).]

\(y=\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} x^{n}, \quad(x+1) y^{\prime \prime}+y^{\prime}=0\)

Text Transcription:

x^2n+1letk=n+1

y=sum_n=1^inftyfrac(-1)^n+1nx^n,(x+1)y^prime\prime+y^prime}=0

ANSWER:

Step 1 of 3 

In this problem we have to verify the given power series is a solution of the indicated differential equation.

Given power series is

Given differential equation

 

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