We have attempted to write a concise modern treatment of differential equations emphasizing applications and containing all the core parts of a course in differential or quarter course in differential equations is taught to most engineering students (and many science students) at all universities, usually in the second year. Some universities have an earlier brief introduction to differential equations and others do not. Some students will have already seen some differential equations in their science do not assume any prior exposure to differential equations. The core of the syllabus consists of Chapters 1 and 2 on linear differential equations. The use of Laplace transforms to solve.