On closed-form solutions to a class of ordinary differential equations

Abstract

In this paper,closed-form solutions in terms of integral(s) to any second and third order linear non-homogeneous constant-coe‐cient ordinary difierential equations as well as the second order non-homogeneous Cauchy-Euler equation, are derived. The method is generalized for n th order linear non-homogeneous constant-coe‐cient ordinary difierential equations. A similar method is used to derive closed-form solutions to second order linear non-homogeneous non- constant coe‐cient ordinary difierential equations. We then demonstrate an application of the method to recurrence relations of the second order.