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Show that the solution of the equation %3D dt ax? satisfying the conditions: (i) T →0 as t→ * (ii) T=0 for x = 0 and x = a for all t>0 (iii) T= x whent= 0 and 0

Show that the solution of the equation %3D dt ax? satisfying the conditions: (i) T →0 as t→ * (ii) T=0 for x = 0 and x = a for all t>0 (iii) T= x whent= 0 and 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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This question is from the subject "Partial differential equation"
. Show that the solution of the equation ƏT ?T at ax? satisfying the conditions: (i) T →0 as t→∞ (ii) T=0 for x = 0 and x = a for all t>0 (iii) T=x when t = 0 and 0 < x < a is 2a T(x, t) = - Σ (-1)"–1 sin x exp[-(nx/a)²t] а n=1
Transcribed Image Text:. Show that the solution of the equation ƏT ?T at ax? satisfying the conditions: (i) T →0 as t→∞ (ii) T=0 for x = 0 and x = a for all t>0 (iii) T=x when t = 0 and 0 < x < a is 2a T(x, t) = - Σ (-1)"–1 sin x exp[-(nx/a)²t] а n=1
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