On one criterion of expressibility of functions of a system of linear differential equations with constant coefficients in the form of linear combinations of derivatives of one function included in this system - Barotov, Dostonjon N.; Barotov, Ruziboy N. (Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie), 2023)
In this paper, we study the problem of expressibility of all functions x1(t), x2(t), . . . , xn(t) included in a given homogeneous system of linear differential equations with constant coefficients x′(t) = A·x(t), in the form of linear combinations of derivatives of only one unknown function xк(t) included in this system. A simple criterion is found for the expressibility of all functions of the system x′(t) = A·x(t), in the form of linear combinations of derivatives xк(t), and its correctness is proved. Based on the proven criterion, an appropriate algorithm was developed and its correctness was substantiated.