Preview Of Differential Equation Graphing - Texas Instruments TI-89 Manual Book

Preview of Differential Equation Graphing

Graph the solution to the logistic 1st-order differential equation y' = .001yù (100ì y). Start
by drawing only the slope field. Then enter initial conditions in the Y= Editor and
interactively from the Graph screen.
Steps
1. Display the
MODE
For mode, select
Graph
.
DIFF EQUATIONS
2. Display and clear the Y= Editor.
Then define the 1st-order
differential equation:
y1'(t)=.001y1ù (100ì y1)
Press p to enter the ù shown above.
Do not use implied multiplication
between the variable and
parentheses. If you do, it is treated as
a function call.
Leave the initial condition yi1 blank.
3. Display the GRAPH FORMATS
dialog box. Then set
,
Labels = ON Solution Method =
, and
RK Fields = SLPFLD
Important: To graph one differential
equation, Fields must be set to
or . If Fields=
SLPFLD FLDOFF
an error occurs when you graph.
4. Display the Window Editor, and
set the Window variables as
shown to the right.
5. Display the Graph screen.
Because you did not specify an initial
condition, only the slope field is
drawn (as specified by
in the
Fields= SLPFLD
dialog box).
FORMATS
176 Chapter 11: Differential Equation Graphing
TI-89
Keystrokes
3
dialog box.
B 6
¸
¥ #
ƒ 8 ¸
¸.0 0 1
Y 1 p c 1 0 0
| Y 1 d ¸
¥ Í
D D B 2
,
Axes = ON
D D B 2
D B 1
.
D B 1 ¸
,
DIRFLD
¥ $
0 D 1 0 D
. 1 D 0 D
· 1 0 D 1 1 0
D 1 0 D · 1 0
D 1 2 0 D
1 0 D 0 D.0 0 1
D 2 0
¥ %
GRAPH
³ ›
TI-92 Plus
Keystrokes
3
B 6
¸
¥ #
ƒ 8 ¸
¸ . 0 0 1
Y 1 p c 1 0 0
| Y 1 d ¸
¥ F
D D B 2
D D B 2
D B 1
D B 1 ¸
¥ $
0 D 1 0 D
. 1 D 0 D
· 1 0 D 1 1 0
D 1 0 D · 1 0
D 1 2 0 D
1 0 D 0 D . 0 0
1 D 2 0
¥ %
Display
Important: With y1'
selected, the
TI-89 / TI-92 Plus will graph
the y1 solution curve, not
the derivative y1'.