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Question
Mathematics
The solution of (dy/dx) = (x2 + y2 + 1/2xy), satisfying y(1) = 0 is given by
Q. The solution of
d
x
d
y
=
2
x
y
x
2
+
y
2
+
1
, satisfying
y
(
1
)
=
0
is given by
4640
223
VITEEE
VITEEE 2014
Differential Equations
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A
hyperbola
B
circle
C
ellipse
D
parabola
Solution:
Given differential equation is
d
x
d
y
=
2
x
y
x
2
+
y
2
+
1
⇒
2
x
y
d
y
=
(
x
2
+
1
)
d
x
+
y
2
d
x
⇒
x
2
x
d
(
y
2
)
−
y
2
d
x
=
(
x
2
x
2
+
1
)
d
x
⇒
∫
d
(
x
y
2
)
=
∫
(
1
+
x
2
1
)
d
x
⇒
x
y
2
=
x
−
x
1
C
⇒
y
2
=
(
x
2
−
1
+
C
x
)
When
x
=
1
,
y
=
0
Then,
0
=
1
−
1
+
C
⇒
C
=
0
∴
The solution is
x
2
−
y
2
=
1
i.e., hyperbola.