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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41839a5e-78a0-4252-a9d0-56abef7c9dc5%2F9e4a83aa-b04e-4f3f-b50a-d272713e92c6%2Fxxetgh6_processed.jpeg&w=3840&q=75)
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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