eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2017-01-13 5 1 1 7 10.12691/ajams-5-1-1 AJAMS2017511 article Nick Z. Zacharis nzach@teipir.gr. 1 Department of Computer Systems Engineering, Technological Educational Institute of Piraeus, Athens, Greece Inspired by the method of undetermined coefficients, this paper presents an alternative method to solve linear differential equations with constant coefficients, using the technique of polynomial long division. Expanding this technique with the exponential shift law enables to solve all types of non-homogeneous differential equations, of where the undetermined coefficients can be applied. http://pubs.sciepub.com/ajams/5/1/1/ajams-5-1-1.pdf undetermined coefficients long division exponential shift law