Generalized Integrating Factor Method Applied for One Dimensional Linear Second Order Ordinary Differ- ential Equations

Abstract

This manuscript introduces the concept of generalized integrating factor for one dimensional linear ordinary differential equations of order n. The procedure is used to address linear second order equations with varying and with constant coefficients, commonly found in many practical problems. The solutions are analytically derived by means of double convolutions. Analytical solutions for the constant coefficient case with different types of continuous and discontinuous excitations are discussed with examples. The concept of Heaviside series is introduced to generalize the solutions for discrete excitations.