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Mathematics
Mathematics
Problem
The differential equation
d
y
d
x
=
6
x
(
x
+
2
)
\displaystyle \frac{dy}{dx}=\frac{6}{x(x+2)}
d
x
d
y
=
x
(
x
+
2
)
6
is subject to the condition
y
(
1
)
=
0
y(1)=0
y
(
1
)
=
0
. Which expression gives
y
y
y
explicitly as a function of
x
x
x
? a)
y
=
ln
(
3
x
x
+
2
)
y=\ln\!\left(\dfrac{3x}{x+2}\right)
y
=
ln
(
x
+
2
3
x
)
b)
y
=
3
ln
(
x
x
+
2
)
y=3\ln\!\left(\dfrac{x}{x+2}\right)
y
=
3
ln
(
x
+
2
x
)
c)
y
=
3
ln
(
3
x
x
+
2
)
y=3\ln\!\left(\dfrac{3x}{x+2}\right)
y
=
3
ln
(
x
+
2
3
x
)
d)
y
=
3
ln
(
x
+
2
3
x
)
y=3\ln\!\left(\dfrac{x+2}{3x}\right)
y
=
3
ln
(
3
x
x
+
2
)
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