This new edition presents the essence of decades of experience of teaching Differential Equations to engineering students of various universities and colleges. It continues the tradition of providing instructors and students with a practical-oriented, step-by-step, logical and easy to understand resource for teaching and learning Differential Equations. Though necessary theory is employed in outlining definitions, formulas, laws etc., the theory is purposely kept to a minimum to keep the focus on understanding through practical problems solving. The intention has been to introduce all the topics through concrete examples, applications and analogies, instead of abstract theoretical arguments. The first chapter of this book have been devoted to Basics of differential equations ,its definition, Order, degree and formations of differential equations, second chapter have been devoted to solutions of differential equations by various method, finding general and particular solution Third chapter deals applications of the differential equations and its solutions. Chapter four deals nth order differential equations, simultaneous differential equations and boundary value problems.