Synopsis The present publication is divided into three sections covering Differential Equations, Special Functions and Integral Transforms. The topics included in the text fully covered the syllabi of several Indian Universities. Section of Differential Equations of the first order but not of the first degree, Singular Solutions, Trajectories, Homogeneous Linear Differential Equations, Simultaneous Linear Differential Equations with Second order with Variable Constant Coefficients, Linear Differential Educations of Second Order with Variable Coefficients, Partial Differential Equations of First of Order with Variable Coefficients, Partial Differential Equations of First Order, Linear Partial Differential Equations with Constant Coefficients and Monge’s Method. Section on Special functions covers Legendre’s Functions, Bessel’s Equations and Bessel’s Functions, while the section on Integral Transforms covers Laplace Transform, The Inverse Laplace Transform, Applications of Laplace Transforms to Differential Equations, Fourier Transform and Examples on Fourier Transforms as their Application to Boundary Value Problems. It is hoped that the publication is of great value to all the students.