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4. If u(x, t) satisfies the wave equation utt = Uxx, prove the identity u(x + h, t+k) + u(x − h, t − k) = u(x + k, t + h) + u(x − k, t − h) for all x, t, h, and k. Sketch the quadrilateral Q whose vertices are the arguments in the identity.

4. If u(x, t) satisfies the wave equation utt = Uxx, prove the identity u(x + h, t+k) + u(x − h, t − k) = u(x + k, t + h) + u(x − k, t − h) for all x, t, h, and k. Sketch the quadrilateral Q whose vertices are the arguments in the identity.

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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4. If u(x, t) satisfies the wave equation Utt = Uxx, prove the identity u(x + h, t + k) + u(x − h, t − k) = u(x + k, t + h) + u(x − k, t – h) for all x, t, h, and k. Sketch the quadrilateral Q whose vertices are the arguments in the identity.
Transcribed Image Text:4. If u(x, t) satisfies the wave equation Utt = Uxx, prove the identity u(x + h, t + k) + u(x − h, t − k) = u(x + k, t + h) + u(x − k, t – h) for all x, t, h, and k. Sketch the quadrilateral Q whose vertices are the arguments in the identity.
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