While studying linear algebra I encountered the following result regarding the solutions of a non homogeneous system of linear equations: if
Where x is a particular solution.
Then, while studying differential equations, I found that the solutions for
are all of the form
Where the last term refers to the solutions of the associate homogeneous equation and is a particular solution.
These two concepts seem related to me, but I've not been able to find/think about a satisfying reason, so I'd like to know whether there is actually a relation or not.
I should specify that I've not been able to study properly systems of differential equations of the first order or equations of the n-th order yet, I suspect that the answer is there but I can't be sure. However I'd like to get the complete answer, so if it involves the latter topics it's not a problem.