These two commands do the same things as `dfieldplot` and
`phaseportrait`, but are more general. In fact,
`dfieldplot` and `phaseportrait` just call
`DEplot1` or `DEplot2` with appropriate
arguments. However, they are more specific in the following sense:
`DEplot1` is only for a single first order differential
equation and `DEplot2` is only for a system of two first order
differential equations. We will consider only autonomous systems
here. For further information, look at the help pages. Optional
arguments that we have described earlier, like `arrows`,
`stepsize`, and
`scene` can also be used with these commands.

The `DEplot1` command has two forms. The first is used to plot
the direction field and a set of trajectories and the second form
plots only the direction field. However, it is also possible to plot
solution trajectories without the direction field. We give examples
below for each behavior for our model, equation (3).

To plot a set of trajectories as well as the direction field, use a command like the following.

> DEplot1(de1,[t,x],t=0..2,[0,1/2],[0,-1/2],[0,2]);

You can also set the range for the dependent variable, but it isn't
required. Instead, Maple computes the trajectories and then sets an
appropriate range for *x*.

To plot only the direction field, you omit the initial conditions and set a range for the dependent variable, like the following.

> DEplot1(de1,[t,x],t=0..2,x=-2..2);

To plot only trajectories without the direction field, use the
optional argument
`arrows=NONE`

. The default value of the `arrows` parameter
is `THIN`, but you can set it to one of the other values given
above for the `phaseportrait` command. Here is an example using
the `arrows=NONE`

option.

> DEplot1(de1,[t,x],t=0..2,[0,1/2],[0,-1/2],[0,2],arrows=NONE);

The syntax for the `DEplot2` command is very similar to that
for `DEplot1`. Again there are two forms, one for plotting
trajectories and the direction field and one for plotting only the
direction field. Just as for `DEplot1`, it is possible to just
plot trajectories.

To plot a set of trajectories as well as the direction field, use a command like the following.

> DEplot2(sys1,[x,y],t=0..1,[0,0,1],[0,1,0]);

If you don't like the ranges that Maple chooses for the dependent variables, you can specify them yourself.

To plot just the direction field, leave out the initial conditions and specify ranges for the two independent variables.

> DEplot2(sys1,[x,y],t=0..1,x=-2..2,y=-2..2);

To omit the direction field and just plot the trajectories, use the
optional argument `arrows=NONE`

. This speeds up the plotting
tremendously.

> DEplot2(sys1,[x,y],t=0..1,[0,0,1],[0,1,0],arrows=NONE);

Thu Oct 24 13:33:53 EDT 1996