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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 25RE
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[Second Order Equations] How do you solve this question?

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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