The ODEPlot command outputs an interactive plot of a 1st order differential equation system of two equations, along with controls to explore and manipulate the plot, or adjust the input ODE or system and its parameters.

The plot itself shows the direction field of the system (if the system is autonomous), and includes a default trajectory through an initial point.

Click on the plot to add more initial points and the corresponding trajectories through those points.

The controls included are as follows:

A combobox that allows you to select from a number of pre-set example ODE systems or choose a custom ODE system.

A math container that shows the equations of the current system being plotted and allows them to be changed.

A set of variable range bound settings that shows and allows for editing the variable range bounds.

A set of parameter settings that shows and allows for editing the system parameters.

A button to clear the set of initial values and corresponding trajectories.

If you provide the extra argument system, ODEPlot plots the given system, and the associated variables and parameters populate the controls.

The optional arguments dependent_variable_ranges specify the bounds of the dependent variables shown in the plot. If not specified, the default range will be from -1 to 1 for each dependent variable.

The optional argument independent_variable_range specifies the bounds of the independent variables used when plotting solution curves. The extent of the values of the independent variable in each solution curve is determined by this option. If not specified, the default range will be from -1 to 1.

parameter_values : If there are any parameters in the given system, you can also supply a corresponding optional argument of the form name = value for each such parameter to specify its current value in the plot. These values can later be adjusted interactively using the controls in the left panel of the output of ODEPlot. The default value for each parameter is 0.

You can also specify a set or list of initial values for the solution curves with the optional argument initial_values. This argument takes the form [t, x, y] = [[t__0, x__0, y__0], [t__1, x__1, y__1], ...] or [t, x, y] = {[t__0, x__0, y__0], [t__1, x__1, y__1], ...}, where t is the independent variable and x and y are the dependent variables. For each point [t__i, x__i, y__i] in this list, a solution curve will be plotted through the point [x__i, y__i] which satisfies the system at the given values of the independent and dependent variables. The bounds of that solution curve will be determined by the bounds of the independent variable specified in the independent_variable_range option. The default set of initial values is a grid of nine points: one at each corner of the plot, one at the midpoint of each edge, and one at the center; the value taken for the independent variable for each point is 0.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{ODEs}\right)\:$

$\mathrm{ODEPlot}\left(\right)$

$\mathrm{ODEPlot}\left(\left\{\mathrm{diff}\left(x\left(t\right)\,t\right)=\exp \left(-y\left(t\right)\right)\,\mathrm{diff}\left(y\left(t\right)\,t\right)=k-x\left(t\right)\right\}\,t=0..5\,y=-2..2\,x=-3..3\,k=-1\,\left[t\,x\,y\right]=\left[\left[0\,1\,2\right]\,\left[0\,-3\,-2\right]\,\left[0\,-2\,0\right]\right]\right)$

The Student[ODEs][ODEPlot] package was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.

The Student[ODEs][ODEPlot] package was updated in Maple 2025.

The system parameter was introduced in Maple 2025.

The dependent_variable_ranges, independent_variable_range, parameter_values and initial_values options were introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.