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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
3-36 Diff erential Equations
3.2.1 Short Methods for Finding the Particular Integrals
in Special Cases
Let
0
() ()
n
nr
r
r
fDy aD y Qx
=
⎛⎞
==
⎜⎟
⎝⎠
(3.37)
be a non-homogenous linear equation, where a
r
are real constants.
We will now consider short methods for fi nding the P.Is in special
cases when Q(x) is of the form (1)
aX
e
(2)
sin or cosax ax
(3)
m
x
(4)
aX
eV
and (5)
,
xV
where V is a function of x.
(1) Q(x) = e
ax
where ‘a’ is a constant
Case (i)
() 0fa
Since
22
,,
ax ax ax ax
D
eaeDeae==
and generally,
rax rax
De ae=
00
() ()
nn
ax n r ax n r ax ax
rr
rr
fD e aD e aa e fae
−−
==
⎛⎞⎛⎞
== = =
⎜⎟⎜⎟
⎝⎠⎝⎠
∑∑
(3.38)
Applying
1
()fD
on both sides of Eq. (3.35)
(
)
⎛⎞
==
⎜⎟
⎝⎠
⎛⎞
⇒=
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Publisher Resources

ISBN: 9781299487406Publisher Website