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Mathematics
Problem
Consider the differential equation
d
y
d
x
=
x
y
\dfrac{dy}{dx}=\dfrac{x}{y}
d
x
d
y
=
y
x
. Which option gives a general family of solutions to the equation? a)
y
=
x
2
+
C
y = \sqrt{x^{2}+C}
y
=
x
2
+
C
b)
y
2
=
x
2
+
C
y^{2}=x^{2}+C
y
2
=
x
2
+
C
c)
y
2
=
1
2
x
2
+
C
y^{2}=\dfrac{1}{2}x^{2}+C
y
2
=
2
1
x
2
+
C
d)
y
2
=
x
3
3
+
C
y^{2}=\dfrac{x^{3}}{3}+C
y
2
=
3
x
3
+
C
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