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Mathematics
Mathematics
Problem
Let
y
(
x
)
y(x)
y
(
x
)
be defined by the differential equation
d
y
d
x
=
x
2
y
2
\dfrac{dy}{dx}=\dfrac{x^{2}}{y^{2}}
d
x
d
y
=
y
2
x
2
with
y
(
1
)
=
2
y(1)=2
y
(
1
)
=
2
. Which of the following gives
y
y
y
explicitly in terms of
x
x
x
? a)
y
(
x
)
=
(
x
3
−
7
)
1
/
3
y(x)=\bigl(x^{3}-7\bigr)^{1/3}
y
(
x
)
=
(
x
3
−
7
)
1/3
b)
y
(
x
)
=
(
3
x
2
+
7
)
1
/
3
y(x)=\bigl(3x^{2}+7\bigr)^{1/3}
y
(
x
)
=
(
3
x
2
+
7
)
1/3
c)
y
(
x
)
=
(
x
3
+
7
)
1
/
3
y(x)=\bigl(x^{3}+7\bigr)^{1/3}
y
(
x
)
=
(
x
3
+
7
)
1/3
d)
y
(
x
)
=
(
x
3
+
7
)
1
/
2
y(x)=\bigl(x^{3}+7\bigr)^{1/2}
y
(
x
)
=
(
x
3
+
7
)
1/2
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