**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