70
Economic Dynamics
We shall return to linear approximations in chapter 3 when considering differ
ence equations, and then again in chapters 4 and 5 when we deal with nonlinear
systems
of differential and difference equations. These investigations will allow
us to use linear approximation methods when we consider economic models in
part II.
2.11 Solving differential equations with
Mathematica
2.11.1
Firstorder equations
Mathematica
has two built in commands for dealing with differential equations,
which are the
DSolve
command and the
NDSolve
command. The Frst is used to
Fnd a symbolic solution to a differential equation; the second Fnds a numerical
approximation. Consider the following Frstorder differential equation
dy
dt
=
f
(
y
,
t
)
In particular, we are assuming that
y
is a function of
t
,
y
(
t
). Then we employ the
DSolve
command by using
DSolve[y’[t]==f[y[t],t],y[t],t]
Note a number of aspects of this instruction:
(1)
The equation utilises the single apostrophe, so
y
±
(
t
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 Fall '11
 Dr.Gwartney
 Economics, Economic Dynamics

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