Determining a Particular Solution for N-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form ea·x·P(x) ·cosnx or eb·x·Q(x)·sinnx

A particular solution for the n-th order linear differential equations with constant coefficients that are free of term such as P(x)· e^a·x ·cosⁿx or/and Q(x)·e^b·x· sinⁿx, n∈ N, can be determined based on two elements: the way in which cosⁿx and sinⁿx can develop, and, on the other hand on the way a particular solution for the free terms P(x) ·e^a·x·cosⁿx or/and Q(x)·e^b·x·sin^mx, n ∈N is sought. We can, of course, write the way a particular solution looks also in the case we have a combination of the two terms or more terms of this kind.