Solution Found!
In by direct substitution that the given power series is a
Chapter 6, Problem 32E(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 \(x^{2 n+1} \text { let } k=n+1\).]
\(y=\sum_{n=0}^{\infty}(-1)^{n} x^{2 n}, \quad\left(1+x^{2}\right) y^{\prime}+2 x y=0\)
Text Transcription:
x^2n+1letk=n+1
y=sum_n=0^infty(-1)^nx^2n,(1+x^2right)y^prime+2xy=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 \(x^{2 n+1} \text { let } k=n+1\).]
\(y=\sum_{n=0}^{\infty}(-1)^{n} x^{2 n}, \quad\left(1+x^{2}\right) y^{\prime}+2 x y=0\)
Text Transcription:
x^2n+1letk=n+1
y=sum_n=0^infty(-1)^nx^2n,(1+x^2right)y^prime+2xy=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 .