Continuous dynamic systems
27
In each of the first three examples there is only one variable other than time,
namely
x
. They are therefore referred to as
ordinary differential equations
. When
functions of several variables are involved, such as
u
and
v
in example (iv), such
equations are referred to as
partial differential equations
. In this book we shall
be concerned only with ordinary differential equations.
Ordinary differential equations are classified according to their order. The
order
of a differential equation is the order of the highest derivative to appear in the
equation. In the examples above (i) and (iii) are firstorder differential equations,
while (ii) is a secondorder differential equation. Of particular interest is the
linear
differential equation
, whose general form is
a
0
(
t
)
d
n
x
dt
n
+
a
1
(
t
)
d
n
−
1
x
dt
n
−
1
+
. . .
+
a
n
(
t
)
x
=
g
(
t
)
(2.2)
If
a
0
(
t
),
a
1
(
t
),
. . .
,
a
n
(
t
) are absolute constants, and so independent of
t
, then
equation (2.2) is a
constantcoefficient
n
thorder differential equation
. Any
differential equation not conforming to equation (2.2) is referred to as a
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 Dr.Gwartney
 Economics

Click to edit the document details