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Mathematics
Problem
A curve satisfies
d
y
d
x
=
x
2
y
\dfrac{dy}{dx}=\dfrac{x}{2y}
d
x
d
y
=
2
y
x
and passes through
(
0
,
1
)
(0,1)
(
0
,
1
)
. Which of the following is its equation? a)
y
2
=
x
2
+
1
y^{2}=x^{2}+1
y
2
=
x
2
+
1
b)
y
2
=
x
2
2
+
1
y^{2}=\dfrac{x^{2}}{2}+1
y
2
=
2
x
2
+
1
c)
y
2
=
x
2
4
+
1
y^{2}=\dfrac{x^{2}}{4}+1
y
2
=
4
x
2
+
1
d)
y
2
=
x
2
2
−
1
y^{2}=\dfrac{x^{2}}{2}-1
y
2
=
2
x
2
−
1
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