The values off (x) and g (x) are, ди f (x) = u (x, 0) and g (x) = dt lt=0 At the given conditions ди u (x, 0) = f (x) and -o = 0, So, the value of g (x) is 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I dont understand why g(x)=0. Can you please explain it to me. Thank you

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Rewrite the term c2c3 = An and c2c4 = B, in
the above equation,
00
пла
пла
u (x, t) = 2 (An cos
t + Bn sin
L
t) sin
n=1
(7)
The value of An is,
L
|f (x) sin 4xdx (8)
пл
An
L
The value of Bn is,
L
Bn
8 (x) sin xdx (9)
пла
The values of f (x) and g (x) are,
f () 3D и (х, 0) and g (x) —
ди
dt \t=0
At the given conditions
u (x, 0) = f (x) and
= 0,
dt It=0
So, the value of g (x) is 0.
Privacy -
II
Transcribed Image Text:LTE 8:37 ¢ Get live help whenever you Try bartleby tutor today need from online tutors! Rewrite the term c2c3 = An and c2c4 = B, in the above equation, 00 пла пла u (x, t) = 2 (An cos t + Bn sin L t) sin n=1 (7) The value of An is, L |f (x) sin 4xdx (8) пл An L The value of Bn is, L Bn 8 (x) sin xdx (9) пла The values of f (x) and g (x) are, f () 3D и (х, 0) and g (x) — ди dt \t=0 At the given conditions u (x, 0) = f (x) and = 0, dt It=0 So, the value of g (x) is 0. Privacy - II
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