Please solution For u(x, t) defined on the domain of 0

Name: Please solution For u(x, t) defined on the domain of 0
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please solution For u(x, t) defined on the domain of 0

Given: To solve: ∂2u∂t2 = ∂2u∂x2+ ∂4u∂x4 + t + cos2x +sinxcost

Answered: For u(x, t) defined on the domain of 0

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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Please solution

For u(x, t) defined on the domain of 0<x< 2n and t20, solve the PDE,
a2u
atu
+t + cos(2x) + sin(x)cos(t)
at2
with periodic boundary conditions in x-direction, and the boundary conditions in the t-direction given as
(i) u(x, 0) = 0
(ii) u¿(x,0) = 0
%3D
We expect a closed form solution that contains only a finite number of terms and with no unevaluated integrals.

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