This book presents the theoretical concepts of methods of solutions of ordinary and partial differential equations as well as equips the students with the various tools and techniques to model different physical problems using such equations. The book discusses the basic concepts of differential equations, different methods of solving ordinary differential equations and the solution procedure for ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The book elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel's and Legendre's equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts. The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics. Table Of Contents: Contents Preface 1.Introduction of Ordinary Differential Equation 2.Differential Equations of the First Order and First Degree 3.Differential Equations of First Order and of Higher Degree 4.Linear Differential Equations with Constant Coefficients 5.Homogeneous Linear Differential Equations with Variable Coefficients 6.Exact Differential Equations and Differential Equations of Higher Order 7.Linear Differential Equations of Second Order 8.Simultaneous L