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.
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.