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SolveOverdeterminedEqs

SolveOverdeterminedEqs[system]
solves a overdetermined system of differential equations.

MORE INFORMATION

To use SolveOverDeterminedEqs, you first need to load the SYM Package using Needs["SYM`"].

The result is a list {{{solution, conditions}, caseAssumptions}...} where the list solution contains the solution of the system in the same fashion as DSolve, conditions includes all the unsolved equations and caseAssumptions, the assumptions on the parameters of the system for the specific solution.

SolveOverdeterminedEqs will terminate when it cannot solve further the system of equations returning the solutions found so far and the remainder of the equations.

SolveOverdeterminedEqs uses at its core the DSolve function. Hence, every augmentation or addition to DSolve will also benefit SolveOverdeterminedEqs.

Although intended for solving the determining equations that arise from the linearization of the symmetry condition, SolveOverdeterminedEqs can be used for any kind of system of differential equations.

When unable to solve the system the same or a simplified one will be returned.

The following options can be given :

	Verbose	$Verbose	whether to explicitly show each step taken for solving the system
	LogFile	False	whether to log the procedure
	ComplexDomain	False	whether to regard the uknown functions as complex
	KnownFunctions	$KnownFunctions	list any functions that will be considered as known
	Assumptions	{}	assumptions to make about the parameters
	ShowReport	True	whether to show the result to a seperate notebook

Using the Verbose option one can verify the procedure taken for solving the system. In seperate notebook(s) each step of the solution process is illustrated.

The constants of integration that appear in the solutions are indicated by the symbol Const and the free functions with FreeFunc.

Basic Examples (5)

Solving a determining system that arises from an ODE

Click for copyable input

An example that will give us different solutions for specific values of the variable n

The last case is the most general one. Use the option ShowReport to suppress the generated notebook that reports the cases that arise.

When the system is underdetermined or nonlinear SolveOverdeterminedEqs will stop and returns its findings.

in the above case the initial system was returned.

An example of a solution which includes also free functions contraint by a differential equation:

The constraint can also be integro-differential:

DSolve

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