b) An insulated uniform bar 2m in length has the temperature of its ends maintained at zero degrees Celsius and at time t = 0. Show that a general solution may be given as 8. U(x, t) = E Qn sin (→)e 2 n=1 Where Qn is found from the initial temperature distribution of the bar. [You do not need to find Qn).

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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Can you please quickly give me full working and answer for Q3B please ??

3.
a) Given that
sin(x – 3t) + cos(x) et,
axdt
where = (t- 4)² when x = 0 and y = In|x| when t =
ay
0,
%3D
ae
find y(x, t).
b) An insulated uniform bar 2m in length has the temperature of its ends maintained at
zero degrees Celsius and at time t = 0. Show that a general solution may be given as
U(x, t) = E Q. sin
()e-t
12
n=1
Where Qn is found from the initial temperature distribution of the bar.
[You do not need to find Q.l.
8.
Transcribed Image Text:3. a) Given that sin(x – 3t) + cos(x) et, axdt where = (t- 4)² when x = 0 and y = In|x| when t = ay 0, %3D ae find y(x, t). b) An insulated uniform bar 2m in length has the temperature of its ends maintained at zero degrees Celsius and at time t = 0. Show that a general solution may be given as U(x, t) = E Q. sin ()e-t 12 n=1 Where Qn is found from the initial temperature distribution of the bar. [You do not need to find Q.l. 8.
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