An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, power series methods, and has an appendix on linear algebra. The book originated to teach Math 286 at the University of Illinois at Urbana-Champaign in the Fall 2008 and Spring 2009 semesters. It has since been successfully used in many university classrooms as the main textbook. See https://www.jirka.org/diffyqs/ or https://jirilebl.github.io/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.