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Mathematics
Problem
Which of the following implicit relations represents a family of solutions to the differential equation
y
d
y
d
x
=
x
y\,\dfrac{dy}{dx}=x
y
d
x
d
y
=
x
? (In each option
C
C
C
is an arbitrary constant.) a)
y
2
=
2
x
+
C
y^{2}=2x+C
y
2
=
2
x
+
C
b)
y
2
=
x
2
+
C
y^{2}=x^{2}+C
y
2
=
x
2
+
C
c)
y
2
=
x
3
3
+
C
y^{2}=\dfrac{x^{3}}{3}+C
y
2
=
3
x
3
+
C
d)
y
2
=
2
x
2
+
C
y^{2}=2x^{2}+C
y
2
=
2
x
2
+
C
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