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Question
Mathematics
The differential equation (dy/dx)= ( √ 1-y2/y) determines a family of circles with
Q. The differential equation
d
x
d
y
=
y
1
−
y
2
determines a family of circles with
3473
223
AIEEE
AIEEE 2007
Differential Equations
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A
variable radii and a fixed centre at
(
0
,
1
)
7%
B
variable radii and a fixed centre at
(
0
,
−
1
)
15%
C
fixed radius
1
and variable centres along the
X
-axis
56%
D
fixed radius
1
and variable centres along the
Y
-axis
22%
Solution:
Given,
d
x
d
y
=
y
1
−
y
2
⇒
∫
1
−
y
2
y
d
y
=
∫
d
x
⇒
−
1
−
y
2
=
x
+
c
⇒
(
x
+
c
)
2
+
y
2
=
1
Here, centre
(
−
c
,
0
)
and radius
=
1