5. Find the series solution for the following wave equation: Uzz = 0, 0 t, Ut u(0, t) = u(L, t) = 0, t> 0, u(z,0) = 6(x – ), u.(z, 0) = 0, 0 < x < L, where 8(r) is the Dirac-delta function with the following property: for any continuous function f(1) in R', | f(x)6(x)dx = 1.

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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5. Find the series solution for the following wave equation:
Utt -
Uzz
0,
0 <x < L,t > t,
u(0, t) = u(L, t) = 0,
t > 0,
u(x, 0) = 6(x – ), u:(x, 0) = 0
0 < x < L,
where 8(x) is the Dirac-delta function with the following property: for any continuous function
f(r) in R',
f(x)8(x)dr = 1.
Transcribed Image Text:5. Find the series solution for the following wave equation: Utt - Uzz 0, 0 <x < L,t > t, u(0, t) = u(L, t) = 0, t > 0, u(x, 0) = 6(x – ), u:(x, 0) = 0 0 < x < L, where 8(x) is the Dirac-delta function with the following property: for any continuous function f(r) in R', f(x)8(x)dr = 1.
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