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Consider the following problem for the wave equation with periodic boundary conditions at a = 0: Sozu = c*0u, (x, t) ER X R., u(0, t) = cos(wt), te R.. a) Find at least one solution. Hint: use the solution guess (*- ct) + n(x+ct) and find a choice of 5,n that fits the BCs. b) Is the solution unique or is there more than one?

Consider the following problem for the wave equation with periodic boundary conditions at a = 0: Sozu = c*0u, (x, t) ER X R., u(0, t) = cos(wt), te R.. a) Find at least one solution. Hint: use the solution guess (*- ct) + n(x+ct) and find a choice of 5,n that fits the BCs. b) Is the solution unique or is there more than one?

Advanced Engineering Mathematics
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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Consider the following problem for the wave equation with periodic boundary conditions at a = 0: Sozu = c8u, (x, t) €R x R,, u(0, t) = cos(wt), te R.. a) Find at least one solution. Hint: use the solution guess E(a- ct) +n(a+ ct) and find a choice of E,n that fits the BCs. b) Is the solution unique or is there more than one?
Transcribed Image Text:Consider the following problem for the wave equation with periodic boundary conditions at a = 0: Sozu = c8u, (x, t) €R x R,, u(0, t) = cos(wt), te R.. a) Find at least one solution. Hint: use the solution guess E(a- ct) +n(a+ ct) and find a choice of E,n that fits the BCs. b) Is the solution unique or is there more than one?
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