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

Abstract

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In this paper,closed-form solutions in terms of integral(s) to any second and third order linear non-homogeneous constant-coefficient ordinary differential 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-coefficient ordinary differential equations. A similar method is used to derive closed-form solutions to second order linear non-homogeneous non- constant coefficient ordinary differential equations. We then demonstrate an application of the method to recurrence relations of the second order.

Keywords: Closed-form, Ordinary Differential Equations, Recurrence Relations