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Question 6. The temperature u(x, t) of a narrow metal rod of length L = π is modelled by the heat equation: 5Uxx Solve the equation if the initial temperature u(x, 0) = x, and the ends of the rod are insulated: ux (0, t) = ux (π, t) = 0, t > 0. Hint: find Fourier cosine series for the function f(x) = x in the initial condition. Ut =

Question 6. The temperature u(x, t) of a narrow metal rod of length L = π is modelled by the heat equation: 5Uxx Solve the equation if the initial temperature u(x, 0) = x, and the ends of the rod are insulated: ux (0, t) = ux (π, t) = 0, t > 0. Hint: find Fourier cosine series for the function f(x) = x in the initial condition. Ut =

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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Question 6. The temperature u(x, t) of a narrow metal rod of length L = π is modelled by the heat equation: Ut = 5Uxx Solve the equation if the initial temperature u(x, 0) = x, and the ends of the rod are insulated: ux uz (0, t) = uz (π, t) = 0, t > 0. Hint: find Fourier cosine series for the function f(x) = x in the initial condition.
Transcribed Image Text:Question 6. The temperature u(x, t) of a narrow metal rod of length L = π is modelled by the heat equation: Ut = 5Uxx Solve the equation if the initial temperature u(x, 0) = x, and the ends of the rod are insulated: ux uz (0, t) = uz (π, t) = 0, t > 0. Hint: find Fourier cosine series for the function f(x) = x in the initial condition.
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