Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients

For n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, with the general solution of n-th homogeneous linear differential equation with constant coefficients attached, to write the general solution of n-th linear differential equation with the given constant coefficients. In all the works that deal with this issue three situations are analyzed: the situation in which the free term is a polynomial P(x), the situation in which the free term is like P(x)· e^α·x and lastly, the situation in which the free term is like e^ω·x · (P(x)· cos(β·x)+ Q(x)·sin(β·x)). In this study we aim to analyze if the free term is a combination of the three cases mentioned.