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142
Chapter 10: Differential Equation Graphing
In
DifEq
graphing mode,
t
is
the independent variable and
n is the equation variable,
Q'
where n ‚ 1 and 9.
Graphing a System of Equations in FldOff Format
For this example, you must transform the fourth-order differential equation
equivalent system of first-order differential equations, as shown in the chart below.
Differentiate...
Define the variables as...
t
=x
Q'1
=y'
Q1
=y
Q'2
=y''
Q2
=y'
Q'3
=y'''
Q3
=y''
(4)
Q'4
=y
Q4
=y'''
Display the mode screen and set
graphing mode.
Display the format screen and set
field format.
Display the equation editor and store the
transformed system of differential
(4)
Lx
equations for y
=e
+y, substituting as
shown in the chart.
Deselect
Q'3
,
Q'2
, and
Q'1
Q'4=e^(Lt)+Q1
only.
- m # # #
DifEq
# " " " b
6 / & #
FldOff
# # # # " "
b
& '
'
# - ‚ D
4
a & E \ '
$ * $ * $ *
to plot
And then substitute:
Q'1
=
Q2
(since
Q'1
=y'=
Q2
Q'2
=
Q3
Q'3
=
Q4
Lt
(4)
Q'4
=e
+
Q1
(since
Q'4
=y
# '
#
2
3
1
(4)
Lx
into an
Ny=e
y
)
Lx
Lt
=e
+y=e
+
Q1
)
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