LinearFunctionalSystems[RegularSolution]  return the regular solution of a linear system of differential equations

Calling Sequence


RegularSolution(sys, vars, opts)
RegularSolution(A, x, case, opts)


Parameters


sys



list of equations; linear differential system

vars



list of function variables such as [y1(x), y2(x), ...]; variables to solve for

A



matrix with rational elements

x



independent variable

case



'differential'; indicates the case of the system

opts



(optional) expression of the form 'point'=p where p is a point at which the solution is to be found





Description


•

The RegularSolution function returns the initial terms of the regular solutions of the specified linear differential system of equations with polynomial coefficients. If such a solution does not exist, then NULL is returned.


The system parameter is entered either in list form (a list of equations sys and a list of function variables vars to solve for), or in matrix form (matrix A and the independent variable x).


The matrix form specifies the system , where L is the differential operator, is the vector of the functions to solve for, and A is a rational matrix.


For the matrix form of the calling sequence, the case of the system must be specified as 'differential'.


The function returns the solutions with the Laurent series involved () being represented as series expansions in x (or in xp if the option 'point'=p is specified). The order term (for example ) is the last term in the series. The function's output is the list of solutions in this form, corresponding to vars.


The solution involves arbitrary constants of the form _c1, _c2, etc.

•

The solution has an attribute which is a table with the following indices:

'initial'  the initial terms of solutions' components

'recurrence'  the recurrences corresponding to solutions' components

'variable'  the independent variable of the given system

'functions'  the independent functions to solve for

'operators'  the operators corresponding to solutions' components

'point'  the point at which to find a solution



1. Regular solutions are to be found only for homogeneous systems

2. Regular solutions are to be found only for differential systems



•

This function is part of the LinearFunctionalSystems package, and so it can be used in the form RegularSolution(..) only after executing the command with(LinearFunctionalSystems). However, it can always be accessed through the long form of the command by using the form LinearFunctionalSystems[RegularSolution](..).



Examples


>


>


 (1) 
>


>


 (2) 
>


 (3) 
>


 (4) 
>


 (5) 
>


>


 (6) 
>


 (7) 


Download Help Document
Was this information helpful?