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## Introduction

In this section we describe Maple commands for plotting direction fields and/or solution curves for either a single first order differential equation of the form

or a two-dimensional autonomous system of the form

There are five Maple commands we will describe here. Four are in the DEtools package, the fifth command is in the plots package. We deal here with only the most basic examples for these commands. To learn about more advanced features, consult the help pages for the individual commands. Here is a list of the five commands we will consider, along with brief descriptions. More complete descriptions and examples follow.

fieldplot
This command is designed to plot a two-dimensional direction field. By using a simple trick, it can be used to plot direction fields for a single first-order differential equation. The syntax for this command is slightly simpler than that of the other commands described here, but it has the defect of producing arrows that are not very good. There is also a fieldplot3d command for plotting three-dimensional direction fields.
dfieldplot
This command will plot the direction field for either a single differential equation or a two-dimensional autonomous system.
DEplot1
Plots the direction field for a single differential equation. Can also be given an list of initial conditions for which to plot solution curves.
DEplot2
Plots the direction field for a two-dimensional autonomous system. Can also be given a list of initial conditions for which to plot solution curves. Will also plot the direction field and solution trajectories for a two-dimensional nonautonomous system.
phaseportrait
Plots solution trajectories for a set of initial conditions. A useful command. Can also include the direction field or use the scene parameter to plot the individual components versus t.

The last four commands do similar things. In fact, DEplot1 and DEplot2 are the fundamental commands and dfieldplot and phaseportrait are convenience functions with simplified syntax that call the lower level routines DEplot1 and DEplot2. We will usually use the higher level routines, so they will be described before DEplot1 and DEplot2.

Next: Examples Up: Plotting direction fields and Previous: Plotting direction fields and

William W. Farr
Thu Oct 24 13:33:53 EDT 1996