Consider the wave problem ∞ < x < ∞, t> 0, 1 – x2, -1 < x < 1, u(x, 0) = f(x) = otherwise, ди (x, 0) = 0. at a) Determine the solution u(x, t) b) Sketch the solution for t =1/2, t = 1, and t = 2.
Consider the wave problem ∞ < x < ∞, t> 0, 1 – x2, -1 < x < 1, u(x, 0) = f(x) = otherwise, ди (x, 0) = 0. at a) Determine the solution u(x, t) b) Sketch the solution for t =1/2, t = 1, and t = 2.
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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Transcribed Image Text:Consider the wave problem
00 < x < ∞,
t > 0,
|1- x2, -1 < I < 1,
u(x,0) = f(x) =
0,
otherwise,
ди
(x, 0) = 0.
a) Determine the solution u(x, t).
b) Sketch the solution for t = 1/2, t = 1, and t = 2.
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