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Byju's Answer
Standard XII
Mathematics
Variable Separable Method
The solution ...
Question
The solution of differential equation
cos
x
.
sin
y
d
x
+
sin
x
.
cos
y
d
y
=
0
is
A
sin
x
sin
y
=
c
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B
sin
x
.
sin
y
=
c
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C
sin
x
+
sin
y
=
c
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D
cos
x
.
cos
y
=
c
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Solution
The correct option is
A
sin
x
.
sin
y
=
c
Given,
(
cos
x
.
sin
y
)
d
x
+
(
sin
x
.
cos
y
)
d
y
=
0
⇒
(
cos
x
.
sin
y
)
d
x
=
−
sin
x
.
cos
y
d
y
⇒
cos
x
sin
x
d
x
=
−
cos
x
sin
y
d
y
( All we have done is separated the variables )
⇒
cot
x
d
x
=
−
cot
y
d
y
( Now integrating both the sides we get )
⇒
∫
cot
x
d
x
=
−
∫
cot
y
d
y
⇒
∫
cot
y
d
y
=
−
∫
cot
x
d
x
l
n
sin
y
=
−
l
n
sin
x
+
l
n
C
(
l
n
C is interpretation const. )
l
n
sin
y
=
l
n
1
sin
x
+
l
n
C
l
n
sin
y
=
l
n
C
sin
x
(
∵
l
n
a
+
l
n
b
=
l
n
a
b
)
sin
y
=
C
sin
x
⇒
sin
x
.
sin
y
=
C
Hence, the answer is
sin
x
.
sin
y
=
C
.
'
Suggest Corrections
0
Similar questions
Q.
Let
sin
x
and
sin
y
be roots of the quadratic equation
a
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θ
+
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,
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The solution of the differential equation
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