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Mathematics
Mathematics
Problem
Consider the differential equation
d
y
d
x
=
y
(
1
−
y
K
)
\displaystyle \frac{dy}{dx}=y\left(1-\frac{y}{K}\right)
d
x
d
y
=
y
(
1
−
K
y
)
, where
K
>
0
K>0
K
>
0
is a constant. In its slope field, horizontal line elements are observed along the line
y
=
4
y=4
y
=
4
. Which value of
K
K
K
is most consistent with this observation? a)
K
=
8
K=8
K
=
8
b)
K
=
4
K=4
K
=
4
c)
K
=
16
3
K=\dfrac{16}{3}
K
=
3
16
d)
K
=
16
K=16
K
=
16
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