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Mathematics
Problem
Consider the differential equation
d
y
d
x
=
k
(
1
−
y
)
\dfrac{dy}{dx}=k\,(1-y)
d
x
d
y
=
k
(
1
−
y
)
, where
k
>
0
k>0
k
>
0
. Describe how increasing the value of
k
k
k
affects the overall appearance of its slope field while leaving the equilibrium solution unchanged.
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