# Euler's Method on the TI-86

Given a differential equation, say y' = 3x-y, here is how to make the TI-86 draw an Euler's method solution curve for that differential equation.

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

2. 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

3. Q1' = 3t-Q1, or as the calculator wants it, Q'1=3t-Q1.
4. Now press [GRAPH][Q'(t)=] and enter our differential equation from the last step on the first line:

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

6. 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:

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

8. Finally, press [WIND] to select a suitable window:
1. Set x and y ranges as usual.
2. Set tMin to match what you gave in INITC above.  Usually you will want the range for x and t to be the same.
3. tStep sets how often points are actually drawn.  I'll pick 0.1 for this example.
4. EStep, at the bottom of the window screen, sets how many Euler steps are made for each point actually plotted.  I'll pick 1.

9. Then press [GRAPH].