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Mathematics
Mathematics
Problem
A slope field is generated by a differential equation of the form
d
y
d
x
=
k
x
y
\dfrac{dy}{dx}=kxy
d
x
d
y
=
k
x
y
, where
k
k
k
is a constant. The field shows that the slope at
(
1
,
2
)
(1,2)
(
1
,
2
)
is
6
6
6
, at
(
2
,
1
)
(2,1)
(
2
,
1
)
is also
6
6
6
, and at
(
1
,
1
)
(1,1)
(
1
,
1
)
is
3
3
3
. Determine the value of
k
k
k
.
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