Find the temperature of a thin rod u(x, t) of length L using the heat equationa²uk-ди0 0atSubject to the conditionu(0,t) = 0, u(L, t) = 050xu(x,0) = f(x) = 50 -L0 < x < L

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Find the temperature of a thin rod u(x,t) of length L using the heat equation a2u k ди 0 0 at Subject to the condition u(0,t) = 0, u(L, t) = 0 50x u(x, 0) = f (x) = 50 – L 0 < x < L

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

Find the temperature of a thin rod u(x, t) of length L using the heat equation
a²u
k-
ди
0 <x < L, t>0
at
Subject to the condition
u(0,t) = 0, u(L, t) = 0
50x
u(x,0) = f(x) = 50 -
L
0 < x < L

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