įor high order ODEs, dsolve might succeed in reducing the order of the ODE but not in solving the problem to the end. In the case of a first order ODE of high degree in dy/dx, the solution may also appear in parametric form as x _T = f _T, y _T = g _T, where _T is the parameter and the right hand sides are explicit expressions of _T. Note that dsolve is sensitive to the _EnvExplicit variable used by solve. If no solutions are found, the empty sequence (NULL) is returned.īy default, dsolve returns the answer in explicit form, unless solve is not able to isolate the dependent variable, or its isolation requires the inversion of fractional powers, or the isolation can only be obtained by means of RootOf (as say y x = RootOf . Herein x, y x represent any pair of independent and dependent variables.Ĭlosed form solutions are returned by dsolve as a sequence of explicit y x = F x, c n or implicit F y x, x, c n = 0 equations, where the c n (n=integer) are arbitrary constants. Note that ODEs can also be constructed by applying (differential) operators - see an example at the end of the page.Ĭaveat: if the first argument ODE is a set or list, even with a single element, or ODE is one of the cases output by the casesplit command, the input is treated as an "ODE system" and the output follows the corresponding conventions described in dsolve,system. When extra arguments are given, they can be placed in any order after the first one. Given an ODE, an extra argument indicating the dependent variable is required only when the given ODE involves more than one function being differentiated. For an illustrated description of the interface, see worksheet/interactive/dsolve.
For information on launching the interface (and command-line options), see dsolve/interactive. The interface is suitable as an educational tool it can provide the corresponding Maple commands needed to compute the solution or plot. In addition to the computation of solutions and solution values, plots can also be generated.
The interface is easy to use, with many common options. The ODE Analyzer, a new interactive interface, has been created for numeric and symbolic solutions of ODE and ODE systems. To see what method is being used to solve a given ODE, you can assign the following (see infolevel ): Classification methods are used when the ODE matches a recognizable pattern (that is, for which a solving method is already implemented), and symmetry methods are reserved for the non-classifiable cases. Using symmetry methods, dsolve first looks for the generators of symmetry groups of the given ODE, and then uses this information to integrate it, or at least reduce its order. In the case of a single ODE, dsolve tries to solve it using either classification methods or symmetry methods. In the case of one or a system of ODEs without initial conditions, dsolve also works with anticommutative variables set using the Physics package using the approach explained in PerformOnAnticommutativeSystem.
#Solution of ode series#
Looking for numerical (see dsolve, numeric ) or series solutions (see dsolve, series ) to ODEs or systems of them. Looking for solutions using integral transforms (Laplace, Fourier). Looking for formal solution to a linear ODE with polynomial coefficients. Looking for formal power series solutions to a linear ODE with polynomial coefficients. Solving ODEs or a system of them with given initial conditions (boundary value problems). Looking for closed form solutions for a single ODE (see below), or a system of ODEs (see dsolve, system ). (optional) depends on the type of problem being solved (see below)Īs a general ODE solver, dsolve handles different types of ODE problems. Indeterminate function of one variable, required if ODE contains derivatives of more than one such function Optional, the right-hand side can be subscripted (default value starting with Maple 2023) or traditional (previous Maple versions) Solve ordinary differential equations (ODEs)ĭsolve(, extra_args )
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