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Mathematics
Mathematics
Problem
The differential equation
d
y
d
x
=
(
y
−
1
)
2
\dfrac{dy}{dx}=(y-1)^2
d
x
d
y
=
(
y
−
1
)
2
has an equilibrium solution at
y
=
1
y=1
y
=
1
. Determine whether the solution curve that passes through
(
0
,
2
)
(0,2)
(
0
,
2
)
moves toward or away from the line
y
=
1
y=1
y
=
1
as
x
x
x
increases.
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