(b) Now, consider the inhomogeneous problem dre Fre it =F(1,t), 00 00₂ t> 0. w(z,0) = 0, w(0,1)=0, w(1,1)=0, (4)
(b) Now, consider the inhomogeneous problem dre Fre it =F(1,t), 00 00₂ t> 0. w(z,0) = 0, w(0,1)=0, w(1,1)=0, (4)
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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Transcribed Image Text:(b) Now, consider the inhomogeneous problem
dre
Fu
=
show that
F(z,t), 0<z<l, t>0
0<z<1,
t> 0,
t> 0.
w(z,0) = 0,
w(0,1)=0,
w(1,1)=0,
(1) By seeking a solution in the form
w(z,t) = f(t) sin(jxz)
(4)
w(z,t)=2Σsin(jxz)e¯(j*)² [[1 F(μ, n) sin(jæµ) du dn.
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