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Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
The different...
Question
The differential equation whose general solution is
y
=
A
cos
(
x
+
3
)
,
where
A
is arbitrary constant is
A
cot
(
x
+
3
)
y
1
+
y
=
0
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B
tan
(
x
+
3
)
y
1
+
y
=
0
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C
cot
(
x
+
3
)
y
1
−
y
=
0
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D
tan
(
x
+
3
)
y
1
−
y
=
0
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Solution
The correct option is
A
cot
(
x
+
3
)
y
1
+
y
=
0
Given,
y
=
A
cos
(
x
+
3
)
......(1).
Differentiating both sides w.r.t
x
we get,
⇒
d
y
d
x
=
−
A
sin
(
x
+
3
)
⇒
d
y
d
x
=
−
y
×
sin
(
x
+
3
)
cos
(
x
+
3
)
[ Using (1) ]
⇒
y
1
cot
(
x
+
3
)
+
y
=
0
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