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Byju's Answer
Standard XII
Mathematics
Integrating Factor
Write the int...
Question
Write the integrating factor of the differential equation:
cos
x
d
y
d
x
+
y
=
sin
x
;
0
≤
x
<
π
2
.
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Solution
Suppose we have the first order differential equation
d
y
d
x
+
P
y
=
Q
where
P
and
Q
are functions involving
x
only.
We multiply both sides of the differential equation by the integrating factor
I
which is defined as
e
∫
P
d
x
cos
x
d
y
d
x
+
y
=
s
i
n
x
⟹
d
y
d
x
+
y
sec
x
=
tan
x
Here
P
=
sec
x
Hence, the integrating factor
I
becomes
e
∫
sec
x
d
x
=
e
ln
|
sec
x
+
tan
x
|
=
|
sec
x
+
tan
x
|
=
sec
x
+
tan
x
, because both
s
e
c
x
,
t
a
n
x
are positive in first quadrant.
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Similar questions
Q.
The integrating factor of the differential equation
cos
x
d
y
d
x
+
sin
x
⋅
y
=
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⋅
sec
x
,
(
cos
x
≠
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)
is
Q.
The integrating factor of the differential equation
cos
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(
d
y
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=
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Solve the differential equation:
cos
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+
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Q.
Find the integrating factor for the differential equation
d
y
d
x
+
y
2
√
x
−
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x
=
0
Q.
Let
y
=
y
(
x
)
be the solution of the differential equation
cos
x
d
y
d
x
+
2
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sin
x
=
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