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Given the initial boundary value problem = 9= dx2 x > 0, t > 0, ди (x, 0) = 0, dt u(x, 0) = f(x), x > 0, u(0, t) = 0. that describes a semi-infinite string with fixed end, u(0, t) = 0, ди which is initially at rest, (x, 0) = 0, sketch the solution u(x, t) for 7 t = 0, t = 3' 6' = 2, and t = t 6' 3 if the initial pulse is given by f(x) = { 2, 3 < x < 4, 0, otherwise,

Given the initial boundary value problem = 9= dx2 x > 0, t > 0, ди (x, 0) = 0, dt u(x, 0) = f(x), x > 0, u(0, t) = 0. that describes a semi-infinite string with fixed end, u(0, t) = 0, ди which is initially at rest, (x, 0) = 0, sketch the solution u(x, t) for 7 t = 0, t = 3' 6' = 2, and t = t 6' 3 if the initial pulse is given by f(x) = { 2, 3 < x < 4, 0, otherwise,

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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Given the initial boundary value problem 9- dx2 х> 0, t> 0, ди u(х, 0) %3D f(x), (x, 0) = 0, dt х> 0, u(0, t) = 0. that describes a semi-infinite string with fixed end, u(0, t) = 0, ди which is initially at rest, (x, 0) = 0, sketch the solution u(x, t) dt for 2 t = 6' 1 4 t = 0, 7 , and t = 6' 3 3 if the initial pulse is given by 2, 3 < x < 4, f(x) = { 0, otherwise,
Transcribed Image Text:Given the initial boundary value problem 9- dx2 х> 0, t> 0, ди u(х, 0) %3D f(x), (x, 0) = 0, dt х> 0, u(0, t) = 0. that describes a semi-infinite string with fixed end, u(0, t) = 0, ди which is initially at rest, (x, 0) = 0, sketch the solution u(x, t) dt for 2 t = 6' 1 4 t = 0, 7 , and t = 6' 3 3 if the initial pulse is given by 2, 3 < x < 4, f(x) = { 0, otherwise,
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