Press the keys 1 ENTER . The initial condition is
returned, that is, you see X = 0 and Y = 1. Press
ENTER again and you see X = .2 and Y = 1.
Thus, y = 1 is the value of the approximate solution
at x = 0.2. Every time you press ENTER the next
value will be returned, until X = 1 is reached, when
the screen says Done.
The Program EULERG
The program EULERG finds the numerical approxi-
mate solution to the differential equation
dy
dx
= f (x, y)
with initial condition y(x
0
) = y
0
using Euler’s method
and graphs the approximate solution. Execute the
program EULERG for the differential equation
dy
dx
=
−y + x + 1, y(0) = 1 on the interval [0, 1] by taking
n = 5. (Refer to Example 3 in the text.)
Solution. Input Y
1
= −Y +X +1. Set the dimensions
of the window as [0, 1] by [0, 2]. Execute the program
EULERG. The value x0, or x
0
is requested. Press the
keys
0 ENTER . The value y0, or y
0
is requested.
Press the keys 1 ENTER . The value B is requested.
Press the keys 1 ENTER . The value H is requested.
Press the keys
.
2 ENTER . A graph of the approx-
imate solution appears.
Chapter 12 Project in Text: Predator and Prey
The Program EULERS
The program EULERS finds and graphs the approxi-
mate solution to a system of two first-order differen-
tial equations using Euler’s method. Execute the pro-
gram EULERS for the system of differential equations
dP
dt
= P −0.5P Q,
dQ
dt
= −0.5Q+0.05P Q. (Refer to the
predator and prey project at the end of Chapter 12.)
Solution. Input Y
1
= X − .5XY and Y
2
= −.5Y +
.05XY . Use a window with dimensions [0, 20] by [0, 4].
Always take y
0
= 2, H = 0.1, and N = 100. Take
x
0
= 6.
The Programs
Editing a Program. To edit a program press
PRGM and you will see a list of your programs in
alphabetical order. The first 10 programs are listed
by number, the others by letter. EXEC is highlighted.
Press the cursor key in order to highlight EDIT in
the first line. Now move the cursor next to the desired
program and press the key ENTER . The program
will appear and the cursor will be on the first line.
To insert something first press 2nd INS and then
insert the symbols you wish. If you need a new line,
then place the cursor at the beginning of a line at a
place you wish to have a new line. Then press 2nd
INS ENTER and a new line will appear.
Quiting a Program. Pressing the keys 2nd QUIT
will get you out of a program and back to the home
screen whether you are editing or have just run a pro-
gram.
Writing a New Program. To write a new program
press the keys PRGM ENTER . You can
type the name of the program and then the program.
Using LINK. If somebody else already has a program
that you want, you can use LINK to transfer their pro-
grams on their TI-82 to your TI-82. Consult the Guide-
book that came with your calculator. Note that you
can transfer programs from a TI-82 to a TI-83, but not
from a TI-83 to a TI82.
Executing a Program. To execute a program press
PRGM and you will see a list of your programs.
EXEC is highlighted. Press the number key or letter
key corresponding to the program you wish to execute.
Press ENTER and the program is executed. You can
also move the cursor next to the program you wish to
execute and press the key ENTER .
To get you started we not only list the first program
50
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