This command is not specifically for direction fields, but is for
plotting two dimensional vector fields. However, this is exactly what
we need to plot the direction field for a two dimensional autonomous
system, since the vector field is tangent to the solutions of equation
(2). That is, this vector field *is* the direction
field.

Since a trick is needed to get `fieldplot` to plot direction
fields for a single first order differential equation, we start with
our our two-dimensional model, equation (4). The commands
below will plot the direction field for and . Note that the `plots` package has to be loaded
first, but you only need to do this once per session.

> with(plots):

> fieldplot([y,-4*x],x=-2..2,y=-2..2);

The first argument to `fieldplot` is always the vector
field. It has to be in the form of a Maple list, that is, a sequence
of comma-separated items enclosed in square brackets. Order is
important in a list, so you should always put first and
second.

To plot the direction field for a single first order differential
equation, we introduce a dummy variable *s* and write equation
1 as the two dimensional system

With the initial condition *s*(0) = 0, note that the first equation
can be solved to give *s*(*t*) = *t*, so the solution to equation
(5) is really the same as the solution to equation
(1).

Using this trick, we can plot the direction field for our example, equation 3 with the following command.

> fieldplot([1,sin(x^2)],s=0..5,x=-2..2);

Thu Oct 24 13:33:53 EDT 1996