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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
8-72 Diff erential Equations
kept so while the end A is raised to 40°C. Find the temperature
distribution of the rod at time t.
Ans:
222
1
2401
( , ) 40 sin exp( /225)
315
n
xnx
uxt n ct
n
=
=+−
p
p
p
8. Find the solution of
22 2
/(/)ut c ux∂∂= under the conditions
(a) (0, ) 0 ( , ) forall .
(b) ( ,0) 2sin forall .
ut ult t
nx
ux x
l
==
=
p
Ans:
222
1
(,) 2 sin exp( /).
n
nx
uxt n ctl
l
=
=−
p
p
8.13.5 One-dimensional Wave Equation
Consider the vibrations of an elastic string placed along the x-axis,
stretched to length l between two fi xed points x = 0 and x = l. First we
consider the problem when there is an initial displacement but no ini-
tial velocity (string ...
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Publisher Resources

ISBN: 9781299487406Publisher Website