This course covers several topics in ordinary differential equations. So it covers the following topics: studying series solutions of second order linear differential equations with variable coefficients at ordinary points , applying Laplace transformation to solve linear differential equations, solving linear systems of differential equations by elimination, solving linear homogenous and non- homogenous systems of ordinary differential equations with constant coefficients using eigenvalues and eigenvectors, the study of the stability of linear systems, phase plane portrait and applications of linear systems.