If u(z,0) = f(z) ue(z,0) = 0 u(z, t), u(z,t) → 0 as |z| → 0 Show that f(z+at) + f(z- at) u(z,t) = %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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If
u(x,0) = f(z)
ue(r,0) = 0
u(1,t)
uz(x,t) → 0 as |z|→
Show that
f(r+at) + f(x– at)
u(z,t) =
2
Transcribed Image Text:If u(x,0) = f(z) ue(r,0) = 0 u(1,t) uz(x,t) → 0 as |z|→ Show that f(r+at) + f(x– at) u(z,t) = 2
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