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There exist many problems in engineering and science which are governed by linear or nonlinear ordinary differential equations. The two forms of linear differential equations with variable coefficients which can be reduced to linear differential equations with constant coefficients by using proper substitutions, has been discussed. The linear partial differential equations of second and higher order with constant coefficients. These can be divided into two groups, homogeneous and non-homogenous linear equations. In this book, how to solve such type equations has been elaborately described. In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the benefit of the students