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`.

Thu Oct 24 13:33:53 EDT 1996