Alternative solutions of inhomogeneous second--order linear dynamic equations on time scales

TL;DR

This paper introduces a new method based on reduction of order for solving inhomogeneous second-order linear dynamic equations on time scales, extending classical analysis to difference, quantum, and general dynamic equations.

Contribution

It presents an alternative to variation of parameters, broadening solution techniques for various types of dynamic equations on time scales.

Findings

New reduction of order method for inhomogeneous equations

Extension to difference, quantum, and arbitrary dynamic equations

Broader applicability of solution techniques

Abstract

We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis on $\R$ to a new form for difference equations, quantum equations, and arbitrary dynamic equations on time scales.