Show that u(x, t) = sin wx sinh wt is a solution to Utt + Uxx = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Show that u(x, t) = sin wx sinh wt is a solution to Utt + Uxx = 0.
Prove that D'Alembert's solution of wave PDE equation
utt = 25uxxu(x,0)=g(x), u₂(x, 0) = f(x).
u(x, t) = ½ [g(x − 5t) + g(x+5t)] + + √x+5+ f(s)ds.
x+St
10x-5t
Transcribed Image Text:Show that u(x, t) = sin wx sinh wt is a solution to Utt + Uxx = 0. Prove that D'Alembert's solution of wave PDE equation utt = 25uxxu(x,0)=g(x), u₂(x, 0) = f(x). u(x, t) = ½ [g(x − 5t) + g(x+5t)] + + √x+5+ f(s)ds. x+St 10x-5t
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