Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 5 1 2017 1 13 Combining Long Division of Polynomials and Exponential Shift Law to Solve Differential Equations 1 7 EN Nick Z. Zacharis Department of Computer Systems Engineering, Technological Educational Institute of Piraeus, Athens, Greece AJAMS2017511 10.12691/ajams-5-1-1 2016 8 25 2016 12 22 2017 1 11 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.