S sin a, 0 2. Q.6 (a) Find the Fourier cosine transform of f(r) 0,

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Q.6 (a) Find the Fourier cosine transform of f(x) = {
sin a, 0<z < 2.
r > 2.
0.
(b) Use Fourier cosine transform to solve the boundary value problem
Uu - 4uzz = 0,
u(0, t) = 0,
u(x,0) = f(x), u(x, 0) = 0, 0<r< o0,
0 <r< 00, t>0,
t2 0.
where f(x) is given in part (a).
6
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Transcribed Image Text:Q.6 (a) Find the Fourier cosine transform of f(x) = { sin a, 0<z < 2. r > 2. 0. (b) Use Fourier cosine transform to solve the boundary value problem Uu - 4uzz = 0, u(0, t) = 0, u(x,0) = f(x), u(x, 0) = 0, 0<r< o0, 0 <r< 00, t>0, t2 0. where f(x) is given in part (a). 6 ,י/ו
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