Solution Found!
In 13 and 14 verify by direct substitution that the given
Chapter 6, Problem 33E(choose chapter or problem)
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