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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
Integration in Series 6-13
where
2
2.uxtt=−
2
1
135 (2 1)
1(2)
246 (2 )
m
m
m
xt t
m
=
⋅⋅
=+
⋅⋅
(6.28)
Now,
1
22
(2 ) [(2 ) (2 )
(1)
(2 ) ( 1) ]
2!
mm mm m m
mmm
utxt t x mx
mm
xt t
=−=
+⋅⋅++−
Substituting in Eq. (6.28), we get
1
211
2
1
22 2
135 (2 1)
(1 2 ) 1 [(2 ) (2 )
246 (2 )
(1)
(2 ) ( 1)
2!
mm
m
mm mm
m
xt t x m x t
m
mm
xt t
−+
=
−+
⋅⋅
−+ =+
⋅⋅
+⋅ ++−
(6.29)
Thus, the coeffi cient
of
n
t
in the expansion
1
2
2
(1 2 )xt t
−+
is
4
2
4
13 (2 1) 13 (2 3)
(2 ) ( 1)(2 )
24 (2) 24 (2 2)
13 (2 5)( 2)( 3)
(2 )
24 (2 4) 2!
135 (2 1) ( 1)
!2(21)
( 1)( 2)( 3)
()
2 4 (2 1)(2 3)
nn
n
nn
n
n
nn
xnx
nn
nnn
x
n
nnn
xx
nn
nn n n
xPx
nn
⋅⋅
−−
⋅⋅−
⋅−−−
++
⋅−
⋅⋅
=−
⋅−
−−
+−=
⋅⋅


212
0
(1 2 ) (
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Publisher Resources

ISBN: 9781299487406Publisher Website