The subject are LDE's with constant coefficients of the following form:

,

and being polynomials of given degrees.

1) I choose the , let it be .

2) I write down the following functions:

every such function satisfies the conditions below:

3) I put down both the source term and the solution function using a base , so that the right side of the equation becomes , and the solution becomes .

4) I make two additional matrices:

,

therefore

5) Finally I rewrite the initial equation:

eventually giving , which can be solved for .

Has such a method been described somewhere, or is it something new?

Thanks in advance