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Mathematics
Problem
Let
x
=
x
(
y
)
x = x(y)
x
=
x
(
y
)
be the solution of the differential equation
2
(
y
+
2
)
log
e
(
y
+
2
)
d
x
+
(
x
+
4
−
2
log
e
(
y
+
2
)
)
d
y
=
0
2(y+2)\log_e(y+2)dx + (x+4-2\log_e(y+2))dy = 0
2
(
y
+
2
)
lo
g
e
(
y
+
2
)
d
x
+
(
x
+
4
−
2
lo
g
e
(
y
+
2
))
d
y
=
0
,
y
>
−
1
y > -1
y
>
−
1
with
x
(
e
4
−
2
)
=
1
x(e^4-2) = 1
x
(
e
4
−
2
)
=
1
. Then
x
(
e
9
−
2
)
x(e^9-2)
x
(
e
9
−
2
)
is equal to (1)
4
9
\frac{4}{9}
9
4
(2)
10
3
\frac{10}{3}
3
10
(3)
32
9
\frac{32}{9}
9
32
(4) 3
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