### Graphing Systems of D.E.s on the TI-82

#### -- a program --

The program is available in two formats.

A binary version that you can load directly
into the graphlink program and download to your calculator. **NOTE:**
If you have trouble downloading this, try holding the shift button on your
keyboard when you click on the link.
A screen shot for those typing in by hand.
#### Instructions for use:

The summary is below. Or you can see a worked-through
example with pictures of actual calculator displays.

- Enter your system as the opening screen instructs (halt the program
if you have already started it by pressing
`[QUIT]`).
- Put
*dx*/*dt* in terms of *x*, *y*, and *t*
in `y1`.
- Put
*dy*/*dt* in terms of *x*, *y*, and *t*
in `y2`.

- Decide whether you want a graph of
*x* vs. *y*, *t*
vs. *x*, or *t* vs. *y*.
- Set your window accordingly.
- Run the program.
- Input initial values for
*t*,* x*, and *y* when asked.
- Input a final value for
*t* and the number of steps desired.
`N=100` is often a good starting place.
- Increase or decrease the value of
`N` to improve accuracy or
speed, respectively.

- When asked, indicate the axes you chose in (2).

#### Notes:

- When the program is done, you can type "
`T`", "`X`",
and "`Y`" (and `[ENTER]`) to get the final values
of each.
- If you run the program a second time, you can input
`A` and
`B` for the initial values of *x*, and *y* to keep the
previous values.
- You can use this for a single differential equation also, with accuracy
much better than a simple Euler's method. For example, to graph a solution
to the initial value problem
*dy*/*dx* = 100-y, *y*(0) = 15:
- Translate to
*dy*/*dt* = 100-y, *y*(0) = 15,
- Enter
`y1=0`, `y2=100-Y`, and give the initial values
for *t* and *y* as 0 and 15 respectively.
- You can give anything at all (e.g. zero) for the inital value of
*x*,
as it will be ignored. Similarly, `y1` can be anything **except**
it must **not** be blank.
- Select "
`GRAPH T VS Y`" and get your graph.

- The program uses a simple trapezoid or order-2 Runge-Kutta iteration.

Last modified April 30, 1997

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