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du 0 0, subject to u(0, t) = 0 u(10, t) = 0 u(x, 0) = 2 – r. Use the method of separation variables to show that the general solution is given by u(x, t) = bn sin () where bn -(1+4(-1)"), n = 1,2, 3,..

du 0 0, subject to u(0, t) = 0 u(10, t) = 0 u(x, 0) = 2 – r. Use the method of separation variables to show that the general solution is given by u(x, t) = bn sin () where bn -(1+4(-1)"), n = 1,2, 3,..

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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Differential equation
3. A uniform rod of length 10 meters is held at both ends. The temperature u(x, t) at any time t of a point P which is r distance away from any of the two endpoints is du Pu 0 < x < 10, t> 0, subject to u(0, t) = 0 u(10, t) = 0 u(x, 0) = 2 – x. Use the method of separation variables to show that the general solution is given by u(x, t) = bn sin 10 n=1 where bn (1+ 4(-1)"), n = 1,2, 3, ...
Transcribed Image Text:3. A uniform rod of length 10 meters is held at both ends. The temperature u(x, t) at any time t of a point P which is r distance away from any of the two endpoints is du Pu 0 < x < 10, t> 0, subject to u(0, t) = 0 u(10, t) = 0 u(x, 0) = 2 – x. Use the method of separation variables to show that the general solution is given by u(x, t) = bn sin 10 n=1 where bn (1+ 4(-1)"), n = 1,2, 3, ...
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