Differential transcendency in the theory of linear differential systems with constant coefficients

TL;DR

This paper explores the reduction of non-homogeneous linear differential systems to simpler forms and investigates the concept of differential transcendency, with applications to Cauchy problems involving constant coefficients.

Contribution

It introduces a method to reduce linear systems to a totally reduced form and applies this to analyze differential transcendency in systems with constant coefficients.

Findings

Reduction of systems simplifies solving Cauchy problems.

New criteria for differential transcendency in linear systems.

Application of reduction techniques to constant coefficient systems.

Abstract

In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.