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Byju's Answer
Standard XII
Mathematics
Variable Separable Method
The solution ...
Question
The solution of
y
d
x
−
x
d
y
=
0
is
A
y
2
=
c
x
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B
y
=
c
x
3
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C
y
=
c
x
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D
x
2
=
c
y
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Solution
The correct option is
C
y
=
c
x
y
d
x
=
x
d
y
=
0
y
d
x
=
x
d
y
∫
d
x
x
=
∫
d
y
y
ln
x
=
ln
y
+
ln
c
ln
(
x
y
)
=
ln
c
⇒
x
y
=
c
y
=
x
c
=
x
c
′
y
=
x
c
′
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0
Similar questions
Q.
Assertion (A): The solution of the equation
x
d
x
+
y
d
y
=
x
d
y
−
y
d
x
x
2
+
y
2
is
2
tan
−
1
y
x
−
1
=
x
2
+
y
2
+
c
Reason (R):
d
(
tan
−
1
y
x
)
=
x
d
y
−
y
d
x
x
y
Q.
Assertion :The solution of
x
+
d
y
d
x
y
−
x
d
y
d
x
=
x
cos
2
(
x
2
+
y
2
)
y
3
is
tan
(
x
2
+
y
2
)
=
x
2
y
2
+
c
Reason:
x
d
x
+
y
d
y
=
1
2
d
(
x
2
+
y
2
)
&
y
d
x
−
x
d
y
y
2
=
d
(
x
y
)
Q.
The greatest value of
c
∈
R
for which the system of linear equations
x
−
c
y
−
c
z
=
0
c
x
−
y
+
c
z
=
0
c
x
+
c
y
−
z
=
0
has a non-trivial solution, is :
Q.
Assertion :Solution of
y
d
x
−
x
d
y
+
x
2
y
2
d
x
=
0
is
3
x
+
x
3
y
=
k
x
, where k is any constant Reason:
y
d
x
−
x
d
y
y
2
=
d
(
x
y
)
Q.
The solution of the differential equation
y
−
x
d
y
d
x
=
a
(
y
2
+
d
y
d
x
)
is
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