Euler's Method on the TI86
Given a differential equation, say y' = 3xy, here is how
to make the TI86 draw an Euler's method solution curve for that differential
equation.

Put the calculator into Differential Equation mode: Press [2nd]
[MODE] and select DifEq as shown:

We must translate the differential equation: In place of the function (y
in
this case), write Q1, and in place of the variable (x in
this case), write t. So we get
Q1' = 3tQ1, or as the calculator wants it, Q'1=3tQ1.

Now press [GRAPH][Q'(t)=] and enter our differential equation
from the last step on the first line:

Press [EXIT][MORE][FORMT] and make sure that, at the bottom
of the screen, both Euler and FldOff are
selected:

Press INITC and enter your initial condition. If
the initial condition was y(1)=4, then since t is
playing the role of x and Q1 is playing the role
of y, we must set tMin=1 and QI1=4:

Press AXES and tell the calculator which axes to graph.
We will always use x=t and y=Q1 in this
class:

Finally, press [WIND] to select a suitable window:

Set
x and y ranges as usual.

Set tMin to match what you gave in INITC
above. Usually you will want the range for x and t
to be the same.

tStep sets how often points are actually drawn. I'll
pick 0.1 for this example.

EStep, at the bottom of the window screen, sets how many
Euler steps are made for each point actually plotted. I'll pick 1.

Then press
[GRAPH].
Last Modified December 7, 1998.
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Janeba's Home Page  Send comments or questions to: mjanebawillamette.edu
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