**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.

If you have a TI Connectivity Cable, you can download the program EULER.83p

**The Program **

:FnOff | {{FnOff is in VARS under Y-Vars} |

:Disp "INITIAL X" | {Disp is in PRGM under I/O} |

:Input X | {Input is in PRGM under I/O} {X is the X,T button} |

:Disp "INITIAL Y" | |

:Input Y | |

:Disp "STEP SIZE" | |

:Input H | |

:Lbl 1 | {Lbl is in PRGM under CTL} |

:0C | {The 0 is a zero}{The arrow is STO } |

:Lbl 2 | |

:X+HU | |

:Y+Y1*HV | {Y1 is in VARS under Y-VARS} |

:Line(X,Y,U,V) | {Line is in DRAW under Draw} |

:UX | |

:VY | |

:IS>(C,20) | {IS> is in PRGM under CTL} |

:Goto 2 | {Goto is in PRGM under CTL} |

:Pause | {Pause is in PRGM under CTL} |

:Goto 1 |

**Running the Program**

You will need to enter a function *f*(x,y) into
Y1 before
running the program. You should also adjust your WINDOW accordingly.
The program will ask for an
initial set of coordinates for X and Y. You will also need to provide
a stepsize. This can be either positive or negative.
The program will plot 20 steps and then pause. Hit
ENTER to plot the next 20 steps, and so on.

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