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Mathematics
Problem
For
d
y
d
x
=
2
x
1
+
y
2
\displaystyle \frac{dy}{dx}=\frac{2x}{1+y^{2}}
d
x
d
y
=
1
+
y
2
2
x
, which relation represents the general implicit solution? a)
arctan
y
=
x
2
+
C
\arctan y = x^{2}+C
arctan
y
=
x
2
+
C
b)
y
3
=
3
2
x
2
+
C
y^{3}=\dfrac{3}{2}x^{2}+C
y
3
=
2
3
x
2
+
C
c)
y
+
1
3
y
3
=
x
2
+
C
y+\dfrac{1}{3}y^{3}=x^{2}+C
y
+
3
1
y
3
=
x
2
+
C
d)
y
+
1
3
y
3
=
1
2
x
2
+
C
y+\dfrac{1}{3}y^{3}=\dfrac{1}{2}x^{2}+C
y
+
3
1
y
3
=
2
1
x
2
+
C
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