Use the finite cosine transform of the fourth derivativ 11 T n²² Fa{f(x)} -[f'(0) - (- p³ p² - f" (0) + (-1)""(p), -F(n) + Fin
Use the finite cosine transform of the fourth derivativ 11 T n²² Fa{f(x)} -[f'(0) - (- p³ p² - f" (0) + (-1)""(p), -F(n) + Fin
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
Solve
![to show that a solution of the boundary-value problem
17. Use the finite cosine transformm of the fourth derivative f"(x),
Fa"(x)} =
n
%3D
F(n) +
P
U'(0) - (-1)"f'(p)]
p2
- "(0) + (-1)"" (p),
atu
u=0, 0<x < T, 0<I< 2, uo conslan
a'u
ax
ar
du
= 0,
axlx=7
du
= 0, 0<1<2
%3D
%3D
0-xe
3D0,
= 0,
= 0, 0<1< 2
%3D
arl
u(x, 0) = 0, u(x, 2) = 0, 0<x < T
%3D
du
au
= Uo, 0<x< T
%3D
at =0
at=2
%D2
%3D
is u(x, t) = } udt³ – 21?).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0cdcac10-a3a0-4140-a355-93434a7b659c%2Faa55d71c-9cd7-49d1-a232-f22802d3ae35%2Fg6hxtwd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:to show that a solution of the boundary-value problem
17. Use the finite cosine transformm of the fourth derivative f"(x),
Fa"(x)} =
n
%3D
F(n) +
P
U'(0) - (-1)"f'(p)]
p2
- "(0) + (-1)"" (p),
atu
u=0, 0<x < T, 0<I< 2, uo conslan
a'u
ax
ar
du
= 0,
axlx=7
du
= 0, 0<1<2
%3D
%3D
0-xe
3D0,
= 0,
= 0, 0<1< 2
%3D
arl
u(x, 0) = 0, u(x, 2) = 0, 0<x < T
%3D
du
au
= Uo, 0<x< T
%3D
at =0
at=2
%D2
%3D
is u(x, t) = } udt³ – 21?).
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