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Solved: In by direct substitution that the given power
Chapter 6, Problem 31E(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 \(x^{2 n+1} \text { let } k=n+1\).]
\(y=\sum_{n=0}^{\infty} \frac{(-1)^{n}}{n !} x^{2 n}, \quad y^{\prime}+2 x y=0\)
Text Transcription:
x^2n+1letk=n+1
y=sum_n=0^inftyfrac(-1)^nn!x^2n,y^prime+2 x y=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 \(x^{2 n+1} \text { let } k=n+1\).]
\(y=\sum_{n=0}^{\infty} \frac{(-1)^{n}}{n !} x^{2 n}, \quad y^{\prime}+2 x y=0\)
Text Transcription:
x^2n+1letk=n+1
y=sum_n=0^inftyfrac(-1)^nn!x^2n,y^prime+2 x y=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 and
Given differential equation .