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Mathematics
Problem
The function
y
y
y
satisfies
d
y
d
x
=
x
sin
(
x
2
)
\dfrac{dy}{dx}=x\sin(x^{2})
d
x
d
y
=
x
sin
(
x
2
)
with the initial condition
y
(
0
)
=
2
y(0)=2
y
(
0
)
=
2
. Which of the following gives an explicit formula for
y
(
x
)
y(x)
y
(
x
)
? a)
y
(
x
)
=
3
−
cos
(
x
2
)
y(x)=3-\cos\left(x^{2}\right)
y
(
x
)
=
3
−
cos
(
x
2
)
b)
y
(
x
)
=
5
2
−
1
2
cos
(
x
2
)
y(x)=\dfrac{5}{2}-\dfrac{1}{2}\cos\left(x^{2}\right)
y
(
x
)
=
2
5
−
2
1
cos
(
x
2
)
c)
y
(
x
)
=
3
2
+
1
2
cos
(
x
2
)
y(x)=\dfrac{3}{2}+\dfrac{1}{2}\cos\left(x^{2}\right)
y
(
x
)
=
2
3
+
2
1
cos
(
x
2
)
d)
y
(
x
)
=
2
−
1
2
cos
(
x
2
)
y(x)=2-\dfrac{1}{2}\cos\left(x^{2}\right)
y
(
x
)
=
2
−
2
1
cos
(
x
2
)
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