determine if the equation is a linear function or not. check yes if it is a linear function and no if it is not. write the degree of the function. for linear function, identify the slope m and the y-intercept b.
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Answer:
order homogeneous linear differential equation, namely the simple growth and decay model
y
′
=
k
y
.
Since first order homogeneous linear equations are separable, we can solve them in the usual way:
y
′
=
−
p
(
t
)
y
∫
1
y
d
y
=
∫
−
p
(
t
)
d
t
ln
|
y
|
=
P
(
t
)
+
C
y
=
±
e
P
(
t
)
+
C
y
=
A
e
P
(
t
)
,
where
P
(
t
)
is an antiderivative of
−
p
(
t
)
.
As in previous examples, if we allow
A
=
0
we get the constant solution
y
=
0
.
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