Slope Fields & Euler's Method on the TI-89

Press <Mode> and select "DIFF EQUATIONS" from the "Graph ..." menu. Press <Enter> to save your choices.


mode screen screenshot

Press <diamond><F1> to access the "y=" screen. Type your differential equation on the "y1' =" line. The independent variable must be "t". The screen shot at right shows the simple differential equation y'(t) = t entered as y1'.
function screen screenshot
Press <F1> to access the "Tools" menu. Select <9> to access the Graph Formats Dialog. You can select either "Euler" or "RK" from the "Solution Method" menu, but be sure that you select "SLPFLD" from the "Fields..." menu. When everything is OK, press <Enter> to save your choices.
graph formats screenshot
Pressing <diamond><F2> accesses the almost-normal window screen. Notice that it contains the parameters t0 (starting t value), tmax (ending t value), and tstep (increment in t) in addition to the normal x and y window dimension parameters. If you find that a graph of your differential equation does not fill the screen, you can adjust the t0 and tmax values. Change tstep to increase/decrease the accuracy (and time taken) of the numerical solution.
Window screen screenshot
Press <diamond><F3> to graph the slope field.
slopefield screenshot
To graph a solution to the differential equation, you need to enter the initial conditions. There are (at least) two ways to do this. The most flexible way is to press <2nd><F3> (F8). The calculator will prompt you to enter a value for "t" and a value for "y1". Starting at that point, the calculator will generate a numerical solution using either the Euler or the Runge-Kutta algorithm (which you selected from the Graph Formats Dialog (<F1> <9>) in step 2 above. You may press <2nd><F3> as many times as you like to plot multiple solutions on the same screen.
An alternate method for supplying initial conditions is on the "y=" screen (<diamond><F1>). If you enter a value for "yi1 =" (directly under the "y1' = " line), this value will be used as an initial value at t = 0. In other words, in the screen shot at right the initial conditions are t = 0, y = 2. You can enter multiple initial conditions using a list: {2, 4, 6} for example.
y= screenshot

last update December 10, 2008 by JL Stanbrough