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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
8-66 Diff erential Equations
2
3
23
0
3
333 33
cos
2
()
sin cos
(2) (2)
22 8
0 0 (( 1) 1) , ( : odd).
n
n
l
nn
nn
n
l
px
lx x
lp
px px
lx
pp
l
n
ln n
⎛⎞
=−
⎜⎟
⎝⎠
⎛⎞
−− +−
⎜⎟
⎝⎠
⎡⎤
=+− −−=
⎢⎥
⎣⎦
a
aa
pp
Hence the temperature distribution in the bar is given by
2
22
33 2
1
(2 1)
81 (21)
(,) sin exp
(2 1)
n
nx
n
uxt at
nl l
=
⎛⎞
=−
⎜⎟
⎝⎠
p
a
p
p
Example 8.13.10 F
ind the temperature in a thin metal rod of length l
with both ends insulated and with initial temperature in the rod sin
(p x/
l ).
Solution The initial boundary value problem consists of the following
1. Partial differential equation for conduction of heat
2
2
2
uu
a
tx
∂∂
=
∂∂
(8.402)
2. Boundary conditions: (Insulation at both ends)
0
0;
x
u
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Publisher Resources

ISBN: 9781299487406Publisher Website