This preview shows page 1. Sign up to view the full content.
38
Economic Dynamics
Step 2
Calculate the
integrating factor
µ
(
t
)
=
e
±
p
(
t
)
dt
Step 3
Multiply throughout by the integrating factor, integrate both sides and add
a constant of integration to the righthand side
(a)
µ
(
t
)
²
dy
dt
+
p
(
t
)
y
³
=
µ
(
t
)
g
(
t
)
or
d
dt
[
µ
(
t
)
y
]
=
µ
(
t
)
g
(
t
)
(b)
´
d
dt
[
µ
(
t
)
y
]
dt
=
´
µ
(
t
)
g
(
t
)
dt
+
c
Step 4
Write the general result
µ
(
t
)
y
=
´
µ
(
t
)
g
(
t
)
+
c
Example 2.10
As an example, let us apply this fourstep procedure to the equation
dy
dt
=
a
+
by
Step 1
We can write this in the standard form
dy
dt
−
by
=
a
Step 2
Calculate the integrating factor
µ
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

Click to edit the document details