Determining a Particular Solution for Systems of Linear Differential Equations with Constant Coefficients that Have on the Column of Free Terms Functions Such As ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx

The determination of a particular solution for the systems of linear differential equations with constant coefficients that have on the column of free terms functions such as e^a·x·P(x) ·cosⁿx or e^b·x·Q(x)·sinⁿx, or/and e^b·x·Q(x) sinⁿx, n ∈ N, is based on the expansion of cosⁿ x and sinⁿ x, and, on the other hand, on how a particular solution for a column of free terms with functions such as e^a·x·P(x) ·cosⁿx or e^b·x·Q(x)·sinⁿx, n ∈ N, looks like. We can also write the way a particular solution looks like when we have a combination of two or more functions on the form e^a·x·P(x) ·cosⁿx or e^b·x·Q(x)·sinⁿx, n ∈ N in the column of free terms.