# SolveOverdeterminedEqs

 SolveOverdeterminedEqs[system] solves a overdetermined system of differential equations.
• 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.
• 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.
Solving a determining system that arises from an ODE
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An example that will give us different solutions for specific values of the variable n
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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.
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in the above case the initial system was returned.

An example of a solution which includes also free functions contraint by a differential equation:
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The constraint can also be integro-differential:
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 Options   (1)