What is Analysis of differential equations?

Analysis of differential equations involves studying the properties and behaviors of equations that relate a function to its derivatives. This field encompasses various methods for solving ordinary differential equations (ODEs) and partial differential equations (PDEs), as well as examining existence, uniqueness, and stability of solutions. Techniques such as qualitative analysis, numerical approximation, and transform methods are commonly employed to understand the dynamics described by these equations in diverse applications across physics, engineering, and Biology. Ultimately, the goal is to gain insights into how systems evolve over time or space based on their governing equations.