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5. [. . 1 ' The solution of the heat equation wrz = wt, 0

5. [. . 1 ' The solution of the heat equation wrz = wt, 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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1 ' The solution of the heat equation wzz =wt, 0 <x < L, which satisfies the boundary 5. [. . conditions w(0, t) = w(L,t) = 0, has the form a?n?n? w(x, t) = bn sin L? e n=1 Find the solution u(x, t) of uzr u(0, t) = 4, u(3, t) = 1, and the initial condition u(x, 0) = 5. Write down the complete solution u(x, t) and expand by giving the first two nonzero terms of the sigma-sum. jut, 0<x < 3, which satisfies the boundary conditions
Transcribed Image Text:1 ' The solution of the heat equation wzz =wt, 0 <x < L, which satisfies the boundary 5. [. . conditions w(0, t) = w(L,t) = 0, has the form a?n?n? w(x, t) = bn sin L? e n=1 Find the solution u(x, t) of uzr u(0, t) = 4, u(3, t) = 1, and the initial condition u(x, 0) = 5. Write down the complete solution u(x, t) and expand by giving the first two nonzero terms of the sigma-sum. jut, 0<x < 3, which satisfies the boundary conditions
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