DefinitionIntroduction to differential equations - Differential equations (DE) are mathematical equations that relate a function (unknown function) with its derivatives (known function), typically representing rates of change, growth, or decay in physical and natural phenomena. The types of differential equations that we will discuss shortly can be classified as ordinary differential equations (ODE) (which contain one independent variable) or partial differential equations (PDE)(which involve more than one independent variable). They are applied in physics, engineering, biology, and economics for modeling dynamical systems, processes and behaviors. The solutions to the differential equations tell us how the systems evolve in time and space. For instance, the differential equation of dx2d2y+ω2y=0 represents simple harmonic motion, where y = displacement, ω = angular frequency, and x = time.
