Function u(x,t) at an interval is given by the partial differential equation u = u, – 3u , 00. %3D Boundary conditions are given by u. (0,t) = u, (7,t) =0. Start conditions are given by u(x,0) = cos (x). Use the Laplace transform to find the u (x, t) that satisfies the boundary conditions and the start condition.
Function u(x,t) at an interval is given by the partial differential equation u = u, – 3u , 00. %3D Boundary conditions are given by u. (0,t) = u, (7,t) =0. Start conditions are given by u(x,0) = cos (x). Use the Laplace transform to find the u (x, t) that satisfies the boundary conditions and the start condition.
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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Question
![Function u(x,t) at an interval is given by the partial
differential equation
u = u, – 3u , 0<x<n,t>0.
%3D
Boundary conditions are given by
u. (0,t) = u, (x,t) = 0.
Start conditions are given by
u(x,0) = cos' (x).
Use the Laplace transform to find the u (x, t) that
satisfies the boundary conditions and the start
condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13413772-1f00-4cda-8c04-9451fee5646b%2F8797f1f5-b468-4ccc-b1db-0347958ce146%2Fwsbk5x5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Function u(x,t) at an interval is given by the partial
differential equation
u = u, – 3u , 0<x<n,t>0.
%3D
Boundary conditions are given by
u. (0,t) = u, (x,t) = 0.
Start conditions are given by
u(x,0) = cos' (x).
Use the Laplace transform to find the u (x, t) that
satisfies the boundary conditions and the start
condition.
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