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Byju's Answer
Standard XII
Mathematics
Arithmetic Progression
The P.I. of ...
Question
The P.I. of
(
3
D
2
+
D
−
14
)
y
=
13
e
2
x
is:
A
26
x
e
2
x
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B
13
x
e
2
x
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C
x
e
2
x
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D
x
2
2
e
2
x
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Solution
The correct option is
A
x
e
2
x
Let
f
(
D
)
=
3
D
2
+
D
−
14
, which implies
f
m
=
2
=
12
+
2
−
14
=
0
and
f
′
m
=
2
=
12
+
1
=
13
We know that , for equation
(
3
D
2
+
D
−
14
)
y
=
13
e
m
x
, if
f
(
m
)
=
0
and
f
1
(
m
)
≠
0
then the Principal solution is
13
x
e
m
x
f
′
(
m
)
Here
m
=
2
, so we get principal solution as
x
e
2
x
Therefore the correct option is
C
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