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

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 $\mathbb{R}$ to a new form for difference equations, quantum equations, and arbitrary dynamic equations on time scales.

12 pages, to appear in the Journal of Difference Equations and Applications