Nonhomogeneous linear differential equations with higher order constant coefficients

Abstract

This article studies the theoretical foundations of non-homogeneous linear differential equations with high-order constant coefficients and methods for their solution. Methods for determining the general solution of a suitable homogeneous equation, using the characteristic equation method, and finding a particular solution in solving equations of this type are analyzed. The article also shows the role of differential equations in modeling practical problems and illustrates their application through some examples. The results obtained are of great importance in mathematical modeling, analysis of processes in the fields of physics and engineering.