0%) Consider the linear wave equation Utt = - o < x < ∞, t> 0, (2- where c > 0 is speed of the wave. Let G(n) be a suitably smooth function and let n = x + ct, - o < x < x, t> 0. Prove that G(x+ ct) is a solution of the equation (2.1).
0%) Consider the linear wave equation Utt = - o < x < ∞, t> 0, (2- where c > 0 is speed of the wave. Let G(n) be a suitably smooth function and let n = x + ct, - o < x < x, t> 0. Prove that G(x+ ct) is a solution of the equation (2.1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement**
*(20%) Consider the linear wave equation*
\[ u_{tt} = c^2 u_{xx}, \quad -\infty < x < \infty, \; t > 0, \tag{2.1} \]
*where \( c > 0 \) is the speed of the wave. Let \( G(\eta) \) be a suitably smooth function and let*
\[ \eta = x + ct, \quad -\infty < x < \infty, \; t > 0. \]
*Prove that \( G(x + ct) \) is a solution of the equation (2.1).*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb29c8079-1767-4255-a596-f513635c59d0%2Fdf5aaefa-ce6b-4225-b7b8-0fa284c31d70%2Fnbrux6s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
*(20%) Consider the linear wave equation*
\[ u_{tt} = c^2 u_{xx}, \quad -\infty < x < \infty, \; t > 0, \tag{2.1} \]
*where \( c > 0 \) is the speed of the wave. Let \( G(\eta) \) be a suitably smooth function and let*
\[ \eta = x + ct, \quad -\infty < x < \infty, \; t > 0. \]
*Prove that \( G(x + ct) \) is a solution of the equation (2.1).*
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