Differential equations are indispensable to physics because they provide the mathematical framework for describing how physical quantities vary with time and position. Newton’s second law of motion, for example, leads to differential equations that allow us to determine the motion of bodies under the influence of forces, from the trajectory of a projectile to the oscillations of a mechanical system. In thermodynamics, the heat equation describes how temperature distributions evolve through the transfer of thermal energy, while Laplace’s and Poisson’s equations are fundamental to understanding electrostatic potentials, gravitational fields and steady-state temperature distributions. Solving these equations often requires powerful mathematical techniques, including Laplace transforms, which convert differential equations into algebraic equations that are frequently much easier to handle. Another important tool is the Green’s function, which provides a systematic way of constructing solutions to linear differential equations subject to specified boundary conditions and external sources. These methods are particularly valuable when dealing with complicated physical systems for which elementary solutions are not readily available. A sound understanding of differential equations and their associated techniques is therefore essential for any aspiring physicist, as they form the foundation upon which much of classical mechanics, electromagnetism and mathematical physics is built.