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Question 3. Suppose the function u(x,t) solves the wave equation utt = Upx, prove che identity u(x + h, t + k) + u(x – h, t – k) = u(x+ k,t+ h) + u(x – k, t – h). To understand this equality, sketch the quadrilateral whose vertices are the points nvolved in this equality).

Question 3. Suppose the function u(x,t) solves the wave equation utt = Upx, prove che identity u(x + h, t + k) + u(x – h, t – k) = u(x+ k,t+ h) + u(x – k, t – h). To understand this equality, sketch the quadrilateral whose vertices are the points nvolved in this equality).

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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Question 3. Suppose the function u(x, t) solves the wave equation utt = Ura, prove the identity u(x +h, t+ k) + u(x – h, t – k) = u(x+ k,t +h) + u(x – k, t – h). (To understand this equality, sketch the quadrilateral whose vertices are the points involved in this equality).
Transcribed Image Text:Question 3. Suppose the function u(x, t) solves the wave equation utt = Ura, prove the identity u(x +h, t+ k) + u(x – h, t – k) = u(x+ k,t +h) + u(x – k, t – h). (To understand this equality, sketch the quadrilateral whose vertices are the points involved in this equality).
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