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Mathematics
Problem
Let
y
(
t
)
y(t)
y
(
t
)
satisfy
d
y
d
t
=
k
y
(
a
−
y
)
\dfrac{dy}{dt}=ky(a-y)
d
t
d
y
=
k
y
(
a
−
y
)
with
k
>
0
k>0
k
>
0
and
a
>
0
a>0
a
>
0
. If
y
(
0
)
>
a
y(0)>a
y
(
0
)
>
a
, justify why
y
(
t
)
>
a
y(t)>a
y
(
t
)
>
a
for every
t
≥
0
t\ge 0
t
≥
0
.
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