Basic concepts, First-order differential equations, Existences and uniqueness for initial–boundary value problems, Separable variables, Homogeneous equations, Exact equations, Linear equations, Equations of Bernoulli-Ricatti, Substitutions, Picard's methods, Linear differential equations of higher-order, Homogeneous equations with constant coefficients, Method of undetermined coefficients, Method of variation of parameters, Differential equations with variable coefficients, Cauchy-Euler equations, Laplace transform, Applications of Laplace transform to solve ordinary differential equations, Non-homogenous equations.
Main Textbook: Zill, D.G. A First Course in Differential Equations with Modeling Applications, 11th Edition, Cengage Learning, 2017. Nagle, R. K. Saff, E. B. and Snider, A. D. Fundamentals of Differential Equations and Boundary Value Problems, Addison-Wesley Longman, 2000. Subsidiary Books: Edwards, C. H. and Penney, D. E. Elementary Differential Equations with Boundary Value Problems, 6 th Edition, Pearson Prentice Hill, 2008. Ross S.L. Introduction to Ordinary Differential Equations, John Wiley, New York, 1998.