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 3and 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=ë1. ncurves=0.
tmax=10. xmax=10. diftol=.001
tstep=.1 xscl=1.
tplot=0. ymin=ë3.
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.