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 Qn sin (,)eal %3D n=1 Where Qn is found from the initial temperature distribution of the bar. [You do not need to find Qn ).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 16E
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Hello can I have the answer and full working out for Q3B since you have already sent me part A

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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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,