This book is mainly intended as a textbook for students at the Sophomore Junior level majoring in mathematics engineering or the sciences in general The book includes the basic topics in Ordinary Differential Equations normally taught in an undergraduate class as linear and nonlinear equations and systems Bessel functions Laplace transform stability etc It is written with ample exibility to make it appropriate either as a course stressing applications or a course stressing rigor and analytical thinking This book also offers sufficient material for a one semester graduate course covering topics such as phase plane analysis oscillation Sturm Liouville equations Euler Lagrange equations in Calculus of Variations first and second order linear PDE in 2D There are substantial lists of exercises at the ends of chapters A solutions manual containing complete and detailed solutions to all the exercises in the book is available to instructors who adopt the book for teaching their classes Solving linear and nonlinear equations and systems Theoretical aspects and qualitative analysis discussed Substantial list of exercises at the ends of chapters Appropriate for undergraduate and graduate students