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Mathematics
Problem
Consider the differential equation
d
y
d
x
=
x
(
y
−
2
)
\dfrac{dy}{dx}=x(y-2)
d
x
d
y
=
x
(
y
−
2
)
. For the particular solution satisfying
y
(
0
)
=
1
y(0)=1
y
(
0
)
=
1
, on which of the following intervals is the solution increasing? a)
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
only b)
(
−
∞
,
0
)
(-\infty,0)
(
−
∞
,
0
)
only c)
(
−
∞
,
0
)
∪
(
0
,
∞
)
(-\infty,0)\cup(0,\infty)
(
−
∞
,
0
)
∪
(
0
,
∞
)
d) The solution is nowhere increasing.
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