Texas Instruments TI-89 - Example of a 3 Rd-Order Equation

Chapter 11: Differential Equation Graphing 189
11DIFFEQ.DOC TI-89/TI-92 Plus: Differential Equation (English) Susan Gullord Revised: 02/23/01 11:04 AM Printed: 02/23/01 2:15 PM Page 189 of 26
1. Press
3
and set
Graph=DIFF EQUATIONS
.
2. Define a system of equations
for the 3rd-order equation as
described on page 186.
Rewrite the equation and
make the necessary
substitutions.
3. In the Y= Editor (
¥#
),
enter the system of
equations.
4. Enter the initial conditions:
yi1=0
,
yi2=1
, and
yi3=1
5. Be sure that only
y1'
is
selected. Use
†
to deselect
any other equations.
6. Press:
ƒ
9
—
or
—
TI
-
89:
¥ Í
TI
-
92 Plus:
¥
F
Set
Axes = ON
,
Labels = ON
,
Solution Method = RK
, and
Fields
=
FLDOFF
.
7. In the Y= Editor, press:
TI
-
89
:
2‰
TI
-
92 Plus:
‰
Set
Axes = TIME
.
8. In the Window Editor
(
¥$
), set the
Window variables.
t0=0. xmin=
ë
1. ncurves=0.
tmax=10. xmax=10. diftol=.001
tstep=.1 xscl=1.
tplot=0. ymin=
ë
3.
ymax=3.
yscl=1.
9. Display the Graph screen
(
¥%
).
Example of a 3rd-Order Equation
For the 3rd-order differential equation y'''+2y''+2y'+y = sin(x),
write a system of equations to enter in the Y= Editor. Then
graph the solution as a function of time. Use initial conditions
y(0) = 0, y'(0) = 1, and y''(0) = 1.
Example
Note: t0 is the time at which
the initial conditions occur.
By default, t0=0.
Important: For 3rd- or
higher-order equations, you
must set
Fields=
FLDOFF
.
Otherwise, an
Undefined
variable
error occurs when
graphing.
Note: With
Axes=
TIME
, the
solution to the selected
equation is plotted against
time (t).
Tip: To find the solution at a
particular time, use
…
to
trace the graph.
y''' + 2y'' + 2y' + y = sin(x)
y''' = sin(x)
ì
2y''
ì
2y'
ì
y
y''' = sin(t)
ì
2y''
ì
2y'
ì
y
y''' = sin(t)
ì
2y3
ì
2y2
ì
y1
y3' = sin(t)
ì
2y3
ì
2y2
ì
y1
Important:
The solution to the y1'
equation is the solution to the 3rd-
order equation.