An Ordinary Differential Equation (ODE) is a mathematical equation that involves an unknown function of a single independent variable and one or more of its derivatives.
These equations are an important components of mathematical modeling, providing the language to describe systems that change continuously, such as population dynamics, planetary orbits, electrical circuits, and chemical reactions.
The solution to an ODE is not a number, but rather a function that satisfies the equation.
Often, an ODE is paired with initial conditions in an Initial Value Problem (IVP) to identify a unique solution that matches a specific starting state of the system.
ODEs are classified by their order (the highest derivative present), and whether they are linear or nonlinear.
Studying ODEs involves finding analytical or numerical solutions to understand and predict the behavior of these dynamic systems, making them indispensable in science and engineering.
BRUNTON, Steve, ME 564 / 565 - Mechanical Engineering Analysis, University of Washington.