# EULER (Graphical Version) - Casio 9800

Introduction
This program plots an approximate solution for the differential equation  using Euler's method. These solutions can be superimposed on a slopefield by running the Slope Field program first. Previous graphs are not cleared for comparison purposes.

If you have not used one of the programs posted on this website before, you should read through the information in the Intro to Programming section first.

The Program
 'EULER' {'   is in ALPHA} {This is the name of the program} "INITIAL X"?X {" is in ALPHA} {?   is in PRGM} { is on the   ,   button} "INITIAL Y"?Y "STEP SIZE"?H "ITERATIONS"?N Lbl 1 {Lbl is in PRGM under JMP} X+HU Y+Y1 H V {Y1 is in VAR under GPH, then followed by a 1} Plot X,Y {Plot is in SHIFT} Plot U,V Line {Line is in SHIFT} UX VY Dsz N {Dsz is in PRGM under JMP} Goto 1 {Goto is in PRGM under JMP}

Running the Program

You will need to enter a function  f(x,y) into Y1 before running the program. You should also adjust your RANGE accordingly. The program will ask for an initial set of coordinates for X and Y and a stepsize. The stepsize can be either positive or negative. You will also need to enter the number of iterations (or steps) you would like to plot. To view the graph after it is plotted use the GT button.

To test the program try the following:
f(x,y)  =  x + y,
WINDOW: -4< x <4,  -4< y <4,
Initial X  =  0,  Initial Y  =  0,
Stepsize  =  0.05
Iterations  = 20