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Mathematics
The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is
Q. The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is
4335
119
KCET
KCET 2019
Differential Equations
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A
2
lo
g
y
=
x
2
+
1
26%
B
2
lo
g
x
=
y
2
−
1
28%
C
2
lo
g
x
=
y
2
+
1
24%
D
2
lo
g
y
=
x
2
−
1
22%
Solution:
d
x
d
y
=
x
y
y
1
d
y
=
x
d
x
I
n
t
e
g
r
a
t
e
l
o
g
y
=
2
x
2
+
c
…
(
1
)
Eq
u
a
t
i
o
n
(
1
)
p
a
ss
in
g
t
h
ro
ug
h
(
1
,
1
)
l
o
g
(
1
)
=
2
1
2
+
C
0
=
2
1
+
c
c
=
−
2
1
l
o
g
y
=
2
x
2
−
2
1
2
l
o
g
y
=
x
2
−
1