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Byju's Answer
Standard XII
Mathematics
Nature of Roots of a Cubic Polynomial Using Derivatives
The particula...
Question
The particular integral of
d
2
y
d
x
2
+
d
y
d
x
=
x
2
+
2
x
+
4
is
A
x
3
3
+
x
2
+
4
x
+
C
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B
x
3
3
+
x
2
+
C
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C
x
3
3
+
4
x
+
C
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D
x
2
+
4
x
+
C
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Solution
The correct option is
C
x
3
3
+
4
x
+
C
Given equation is of the form
(
D
2
+
D
)
y
=
x
2
+
2
x
+
4
∴
P
.
I
.
=
1
D
(
D
+
1
)
(
x
2
+
2
x
+
4
)
=
1
D
(
1
+
D
)
−
1
(
x
2
+
2
x
+
4
)
=
1
D
(
1
−
D
+
D
2
−
.
.
.
)
(
x
2
+
2
x
+
4
)
=
1
D
[
x
2
+
2
x
+
4
−
(
2
x
+
2
)
+
2
]
=
∫
(
x
2
+
4
)
d
x
=
x
3
3
+
4
x
+
C
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