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요 0t2 u (x,t) - 4 1 (02 (2,1)) - 0 u(x,t)

요 0t2 u (x,t) - 4 1 (02 (2,1)) - 0 u(x,t)

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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The PDE 8² u (x, t) – 4 (32 4 (022 u (2,1)) Ət2 where c = 2 Solve the PDE with the initial conditions can be solved using D'Alembert method. That is, it has a solution of the form u(x, t) = (x + ct) + (x − ct), u (x,0) = x², ut (x,0) = 3 cos (x). = 0 Enter the expression for u(x, t) in the box below using Maple syntax. u(x, t) = (x+t)^2-(3/4)*(2sin(x)*cos(x) Note: the expression should be in terms of x and t, but not c.
Transcribed Image Text:The PDE 8² u (x, t) – 4 (32 4 (022 u (2,1)) Ət2 where c = 2 Solve the PDE with the initial conditions can be solved using D'Alembert method. That is, it has a solution of the form u(x, t) = (x + ct) + (x − ct), u (x,0) = x², ut (x,0) = 3 cos (x). = 0 Enter the expression for u(x, t) in the box below using Maple syntax. u(x, t) = (x+t)^2-(3/4)*(2sin(x)*cos(x) Note: the expression should be in terms of x and t, but not c.
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