Primarily designed as a textbook for the first-year undergraduate students of all branches of engineering in various technical universities of India, the second edition of the book maintains to present the ordinary differential equations of first order and higher orders along with their applications, as in the previous edition, but with significant additions. These changes are intended to provide updated information on the key concepts. The text explicates solutions to differential equations in terms of series and applications of Bessel’s function and Legendre’s function. As the book advances, it deals with the Laplace transform and Fourier series in an easy-to-comprehend manner. The book also explains partial differential equations along with their applications such as wave equations, heat equations and transmission line equations. In addition, it describes the method of separation of variables for solving partial differential equations. This book serves as a text to attack various engineering problems which are modelled in the shape of differential equations