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Problem 4: Solve the nonhomogeneous wave equation c2urz +F(x,t) = utt, 0 < x < L, t> 0, u(0, t) = 0, u(L, t) = 0 u(x,0) = f(x), u(x, 0) = 0

Problem 4: Solve the nonhomogeneous wave equation c2urz +F(x,t) = utt, 0 < x < L, t> 0, u(0, t) = 0, u(L, t) = 0 u(x,0) = f(x), u(x, 0) = 0

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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Problem 4: Solve the nonhomogeneous wave equation curr + F (x, t) = utt, 0 < x < L, t > 0, u(0, t) = 0, u(L, t) = 0 u(x, 0) = f(x), ut(x, 0) = Problem 5: The problem of the vibration of an elastic membrane, deoted by u(p, ø, t), fixed on a circular frame can be described by 1 ди 1 02u 0 < p< a, 0 < ¢ < 27, t > 0, Op?' pdp ' p2 d62 u(0, 6, t) is finite, u (а, ф, t) %3D 0 u(р,0, t) 3 и(р, 2т, t), Us(p, 0, t) = us(e, 27, t) u(p, 0,0) = f(p, ), Ut(p, 0,0) = 0 Solve it.
Transcribed Image Text:Problem 4: Solve the nonhomogeneous wave equation curr + F (x, t) = utt, 0 < x < L, t > 0, u(0, t) = 0, u(L, t) = 0 u(x, 0) = f(x), ut(x, 0) = Problem 5: The problem of the vibration of an elastic membrane, deoted by u(p, ø, t), fixed on a circular frame can be described by 1 ди 1 02u 0 < p< a, 0 < ¢ < 27, t > 0, Op?' pdp ' p2 d62 u(0, 6, t) is finite, u (а, ф, t) %3D 0 u(р,0, t) 3 и(р, 2т, t), Us(p, 0, t) = us(e, 27, t) u(p, 0,0) = f(p, ), Ut(p, 0,0) = 0 Solve it.
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