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Q2. Given a partial differential equation Uxx+ Utt = 0 for 0 < x < 1,0

Q2. Given a partial differential equation Uxx+ Utt = 0 for 0 < x < 1,0

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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Q2. Given a partial differential equation Urx + Utt = 0 for 0 <x < 1,0 < t < 1. (a) Solve the given equation with the following conditions U(0,t) = 0,0 <t<1 U (x,0) = 0,0 <x < 1 U (x, 1) = 0,0 < x < 1. %3D Hence, based on your answer from part (a), find the solution of U(x, t) given the condition U(1,t) = t + 1,0 < t < 1. (b)
Transcribed Image Text:Q2. Given a partial differential equation Urx + Utt = 0 for 0 <x < 1,0 < t < 1. (a) Solve the given equation with the following conditions U(0,t) = 0,0 <t<1 U (x,0) = 0,0 <x < 1 U (x, 1) = 0,0 < x < 1. %3D Hence, based on your answer from part (a), find the solution of U(x, t) given the condition U(1,t) = t + 1,0 < t < 1. (b)
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