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Mathematics
Problem
Let
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 of the following is a correct implicit form of the general solution? a)
arctan
y
=
x
2
+
C
\arctan y=x^{2}+C
arctan
y
=
x
2
+
C
b)
y
2
2
+
y
4
4
=
x
2
+
C
\dfrac{y^{2}}{2}+\dfrac{y^{4}}{4}=x^{2}+C
2
y
2
+
4
y
4
=
x
2
+
C
c)
y
+
y
3
3
=
x
2
+
C
y+\dfrac{y^{3}}{3}=x^{2}+C
y
+
3
y
3
=
x
2
+
C
d)
y
+
y
3
3
=
2
x
+
C
y+\dfrac{y^{3}}{3}=2x+C
y
+
3
y
3
=
2
x
+
C
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