On a linear non-homogeneous ordinary differential equation of the higher order whose coefficients are real-valued simple step functions

TL;DR

The paper derives an explicit representation of particular solutions for higher-order linear non-homogeneous ODEs with coefficients as simple step functions, using a method based on infinite-dimensional cellular matrices.

Contribution

It introduces a novel explicit solution method for complex differential equations with piecewise constant coefficients, extending previous matrix-based approaches.

Findings

Explicit solution formulas for higher-order ODEs with step function coefficients

Application of infinite-dimensional cellular matrices to differential equations

Enhanced understanding of solutions with piecewise constant coefficients

Abstract

By using the method developed in the paper [G.Pantsulaia, G.Giorgadze, On some applications of infinite-dimensional cellular matrices, {\it Georg. Inter. J. Sci. Tech., Nova Science Publishers,} Volume 3, Issue 1 (2011), 107-129], it is obtained a representation in an explicit form of the particular solution of the linear non-homogeneous ordinary differential equation of the higher order whose coefficients are real-valued simple functions.