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Differential equations occur in connection with numerous natural phenomena and much of our understanding of nature comes from our ability to solve such equations. Taking note of importance of differential equations, this text is designed to give a simple, lucid, rigorous and comprehensive account of the subject. This book includes almost all the methods for finding solution of ordinary differential equations and partial differential equations with applications. The text also contains the topics of Laplace transforms and Fourier transforms and their applications in finding solutions of differential equations. Divided in three sections the book deals with the following: Section A deals with ordinary differential equations Section B is devoted to study of partial differential equations Section C gives introduction to Laplace and Fourier transforms, Fourier series and their applications in finding solutions of differential equations