**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 **

:FnOff | {FnOff is in GRAPH under Vars} |

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

:Input x | {Input is in PRGM under I/O} {x is the x-VAR} |

:Disp "INITIAL Y" | |

:Input y | {y is in GRAPH under Vars} |

:Disp "STEP SIZE" | |

:Input H | |

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

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

:Lbl Q | |

:x+HU | |

:y+y1*HV | {y1 is in VARS under EQU} |

:Line(x,y,U,V) | {Line is in GRAPH under Draw} |

:Ux | |

:Vy | |

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

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

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

:Goto P |

**Running the Program**

You will need to enter a function *f*(*x,y*) into y1 before
running the program. You can use the x and y shown in the
GRAPH menu. You should adjust the RANGE
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,
RANGE:
-4< x <4,
-4< y <4, Initial x = 0, Initial y = 0,
Stepsize = 0.05