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Mathematics
Problem
The function
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
satisfies
d
y
d
x
=
x
1
+
y
2
\displaystyle \frac{dy}{dx}=\frac{x}{1+y^{2}}
d
x
d
y
=
1
+
y
2
x
and
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
. Which of the following is an implicit equation for the particular solution? a)
y
+
y
3
3
=
x
2
2
−
4
3
y+\dfrac{y^{3}}{3}=\dfrac{x^{2}}{2}-\dfrac{4}{3}
y
+
3
y
3
=
2
x
2
−
3
4
b)
arctan
y
=
x
2
2
+
1
\arctan y=\dfrac{x^{2}}{2}+1
arctan
y
=
2
x
2
+
1
c)
y
+
y
3
3
=
x
2
2
+
4
3
y+\dfrac{y^{3}}{3}=\dfrac{x^{2}}{2}+\dfrac{4}{3}
y
+
3
y
3
=
2
x
2
+
3
4
d)
y
+
y
3
3
=
x
2
+
4
3
y+\dfrac{y^{3}}{3}=x^{2}+\dfrac{4}{3}
y
+
3
y
3
=
x
2
+
3
4
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