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.

    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.
    3. Set your window accordingly.
    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).


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

    Last modified April 30, 1997

    Please mail comments or questions to: mjaneba< at >

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