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Q4. The following Cauchy problem is given. Utt - 4uxx = 0, -00 3, x < 0 x, S1-x², x| < 1 |x| >1 1, u(х, 0) u¿(x, 0) = 0, (a) Is the d'Alembert solution a classical solution? If your answer is NO, determine all the points where the solution is singular. (b) Evaluate u(1, 1).

Q4. The following Cauchy problem is given. Utt - 4uxx = 0, -00 3, x < 0 x, S1-x², x| < 1 |x| >1 1, u(х, 0) u¿(x, 0) = 0, (a) Is the d'Alembert solution a classical solution? If your answer is NO, determine all the points where the solution is singular. (b) Evaluate u(1, 1).

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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Q4. The following Cauchy problem is given. Utt – 4uxx = 0, -00 <x < , 0 <t< o0 0<x<1 1<x< 2 3 — х, 2< х < 3, х> 3, х <0 X, S1- x², 1, u(x, 0) = |x| <1 |지 > 1 ° ut (x, 0) = 0, (a) Is the d'Alembert solution a classical solution? If your answer is NO, determine all the points where the solution is singular. (b) Evaluate u(1,1).
Transcribed Image Text:Q4. The following Cauchy problem is given. Utt – 4uxx = 0, -00 <x < , 0 <t< o0 0<x<1 1<x< 2 3 — х, 2< х < 3, х> 3, х <0 X, S1- x², 1, u(x, 0) = |x| <1 |지 > 1 ° ut (x, 0) = 0, (a) Is the d'Alembert solution a classical solution? If your answer is NO, determine all the points where the solution is singular. (b) Evaluate u(1,1).
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