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Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution curve of the differential equation
d
y
d
x
=
y
x
(
1
+
x
y
2
(
1
+
log
e
x
)
)
\frac{dy}{dx} = \frac{y}{x}(1 + xy^2(1 + \log_e x))
d
x
d
y
=
x
y
(
1
+
x
y
2
(
1
+
lo
g
e
x
))
,
x
>
0
x > 0
x
>
0
,
y
(
1
)
=
3
y(1) = 3
y
(
1
)
=
3
. Then
y
2
(
x
)
9
\frac{y^2(x)}{9}
9
y
2
(
x
)
is equal to: (1)
x
2
5
−
2
x
3
(
2
+
log
e
x
3
)
\frac{x^2}{5 - 2x^3(2 + \log_e x^3)}
5
−
2
x
3
(
2
+
l
o
g
e
x
3
)
x
2
(2)
x
2
2
x
3
(
2
+
log
e
x
3
)
−
3
\frac{x^2}{2x^3(2 + \log_e x^3) - 3}
2
x
3
(
2
+
l
o
g
e
x
3
)
−
3
x
2
(3)
x
2
3
x
3
(
1
+
log
e
x
2
)
−
2
\frac{x^2}{3x^3(1 + \log_e x^2) - 2}
3
x
3
(
1
+
l
o
g
e
x
2
)
−
2
x
2
(4)
x
2
7
−
3
x
3
(
2
+
log
e
x
2
)
\frac{x^2}{7 - 3x^3(2 + \log_e x^2)}
7
−
3
x
3
(
2
+
l
o
g
e
x
2
)
x
2
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