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

#### -- a program --

The program is available in two formats.

• 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.

1. Enter your system as the opening screen instructs (halt the program if you have already started it by pressing [QUIT]).
1. Put dx/dt in terms of x, y, and t in y1.
2. Put dy/dt in terms of x, y, and t in y2.
2. Decide whether you want a graph of x vs. y, t vs. x, or t vs. y.
4. Run the program.
5. Input initial values for t, x, and y when asked.
6. Input a final value for t and the number of steps desired.
1. N=100 is often a good starting place.
2. Increase or decrease the value of N to improve accuracy or speed, respectively.
7. When asked, indicate the axes you chose in (2).

#### Notes:

1. When the program is done, you can type "T", "X", and "Y" (and [ENTER]) to get the final values of each.
2. 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.
3. 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.
4. The program uses a simple trapezoid or order-2 Runge-Kutta iteration.