"This textbook has been designed to meet the needs of B.Sc. Fourth Semester students of Mathematics as per Common Minimum Syllabus prescribed for all Uttar Pradesh State Universities and Colleges under the recommended National Education Policy 2020. To possess an in-depth knowledge of the subjects, topics such as Second Order Linear Differential Equations with Variable Coefficients, Method of Undetermined Coefficients, Variation of Parameters, Series Solutions of Differential Equations, Bessel, Legendre. Hypergeometric Functions and their Properties, Partial Differential Equations of First Order and First Degree and Degree Greater than One, and Solution of Second Order Partial Differential Equations with Variable Coefficients are well explained in Differential Equations. Mechanics part describes the topics such as Mechanics of a Rigid Body, Equilibrium of a System of Forces, Curvilinear Motion and S.H.M., and Motion Under a Central Force in lucid manner.