The Student[ODEs] subpackage is designed to help teachers present and students understand the basic material of a standard first course in ordinary differential equations.  There are two principal component to the subpackage: interactive visualization and step-by-step computation.  These components are described in the next two sections. The package also contains two subpackages as well as additional commands to support the study of ODEs. These are described in the section Computation.

Each command in the Student[ODEs] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.

The long form, Student[ODEs]:-command or Student:-ODEs:-command, is always available. The short form can be used after loading the package.

The Maple Command Completion facility is helpful for entering the names of Student package commands.

Note on boolean options: Many of the commands in the Student[ODEs] subpackage take boolean options, that is, options of the form option_name = value, where value is true or false.  These options are used, for example, to control which components are included in a plot.  In all cases, the form option_name =true can be abbreviated as option_name.

There is one visualization routine, ODEPlot, which is designed to assist in the understanding of plotting the solution of system of ordinary differential equations.

You have considerable control over the presentation of plots produced by the ODEPlot routine. The display of the plot can be adjusted by using a corresponding controls in the left panel.  See the help page for ODEPlot for details.

The ODESteps command produces a step-by-step output showing the solving of various types of ODEs and ODE systems:

Student[ODEs] includes two subpackages. The first, Solve, consists of commands for solving ODEs and systems according to various methods:

The second Student[ODEs] subpackage, ReduceOrder, consists of commands for reducing the order of ODEs using three possible methods:

There are also a number of extra commands which are useful in solving ODEs and systems interactively:

Note that in addition to being a subpackage containing more specific solving commands, Solve acts as a command itself.

To display the help page for a particular Student[ODEs] command, see Getting Help with a Command in a Package.

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

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