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Mathematics
Mathematics
Problem
The direction field for the differential equation
d
y
d
x
=
y
(
1
−
y
5
)
\dfrac{dy}{dx}=y\left(1-\dfrac{y}{5}\right)
d
x
d
y
=
y
(
1
−
5
y
)
indicates that slopes are positive when
0
<
y
<
5
0<y<5
0
<
y
<
5
and negative when
y
>
5
y>5
y
>
5
. For the solution satisfying
y
(
0
)
=
1
y(0)=1
y
(
0
)
=
1
, what is
lim
x
→
∞
y
(
x
)
\displaystyle \lim_{x\to\infty} y(x)
x
→
∞
lim
y
(
x
)
? a)
0
0
0
b)
∞
\infty
∞
c)
5
5
5
d)
2.5
2.5
2.5
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