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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
Partial Diff erential Equations 8-61
1
22
0
2
2
1
24
50 cos sin
22
22
(100 50 ) cos 50 sin
22
0at0 0at0 0at2 0at2
10
xnx nx
nn
nx nx
x
nn
⎡⎤
=− +
⎢⎥
⎣⎦
⎡⎤
⎛⎞⎛⎞⎛⎞
+− +
⎢⎥
⎜⎟⎜⎟⎜⎟
⎝⎠⎝⎠⎝⎠
⎢⎥
⎣⎦
== = =
=−
pp
pp
pp
pp
22
2
22
0 200 2
cos sin 50 cos
22 2
2 400
50 sin sin
22
nn n
nn n
nn
nn
++×
⎛⎞
=
⎜⎟
⎝⎠
pp p
pp p
pp
pp
(8.370)
F
inally, the solution is
22 2
/4
22
1
400 1
(,) 50 sin sin
22
an t
n
nnx
uxt x e
n
=
=+
p
pp
p
(8.371)
Example 8.13.7 An insulated rod of length l has its ends A and B
maintained at 0°C and 100°C, respectively, until steady-state condi-
tions prevail. If B is suddenly reduced to 0°C and maintained at 0°C,
fi nd the temperature at a distance x from A at time t.
[JNTU 2003 (Set 4)]
Solution ...
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Publisher Resources

ISBN: 9781299487406Publisher Website