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Byju's Answer
Standard XII
Mathematics
General Solution of a Differential Equation
Prove that ...
Question
Prove that
x
y
=
l
o
g
y
+
c
is the solution of
d
y
d
x
=
y
2
1
−
x
y
(
x
y
≠
1
)
Open in App
Solution
x
y
=
log
y
+
c
x
d
y
d
x
+
y
=
1
y
d
y
d
x
+
0
d
y
d
x
(
1
y
−
x
)
=
y
d
y
d
x
(
1
−
x
y
y
)
=
y
d
y
d
x
=
y
2
1
−
x
y
Hence proved.
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Similar questions
Q.
Verify that
x
y
=
log
y
+
c
is a solution of the differential equation
(
x
y
−
1
)
d
y
d
x
+
y
2
=
0
.
Q.
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
1.
y
=
e
x
+
1
:
y
′′
−
y
=
0
2.
y
=
x
2
+
2
x
+
C
:
y
′
−
2
x
−
2
=
0
3.
y
=
cos
x
+
C
:
y
′
+
sin
x
=
0
4.
y
=
√
1
+
x
2
:
y
′
=
x
y
1
+
x
2
5.
y
=
A
x
:
x
y
=
y
(
x
≠
0
)
6.
y
=
x
sin
x
:
x
y
=
y
+
x
√
x
2
y
2
(
x
≠
0
a
n
d
x
>
y
o
r
x
<
y
)
7.
x
y
=
log
y
+
C
:
y
′
=
y
2
1
−
x
y
(
x
y
≠
1
)
8.
y
−
cos
y
=
x
:
(
y
sin
y
+
cos
y
+
x
)
y
′
=
y
9.
x
+
y
=
tan
−
1
y
:
y
2
y
′
+
y
2
+
1
=
0
10.
y
=
√
a
2
−
x
2
x
ϵ
(
−
a
,
a
)
:
x
+
y
d
y
d
x
=
0
(
y
≠
0
)
Q.
The solution of
d
y
d
x
=
1
+
y
+
y
2
+
x
+
x
y
+
x
y
2
is
Q.
Prove that
y
2
=
4
a
(
x
+
a
)
is the solution of differential equation
y
×
[
1
−
(
d
y
d
x
)
2
]
=
2
x
d
y
d
x
Q.
Solution of x= 1+xy
(
d
y
d
x
)
+
x
2
y
2
2
!
(
d
y
d
x
)
2
+
.
.
.
.
.
.
.
.
i
s
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