Stepwise Reducibility of the n-th Order Linear Differential Equations with Variable Coefficients

Abstract

This article introduces the concept of gradual (or partial) reducibility of linear differential equations (LDE) with variable coefficients. In this article we construct algorithm for reducing the order of LDE with variable coefficients which after replacing variable has at least one solution of exponential form y(t) = eλt. So reduced equation with new variable coefficients has at least one solution of the eλt form. The second order LDE with variable coefficients is studied in details. The method of solution of LDE by step-by-step reducibility is offered and some specific equations are solved for illustration purposes.