👉 Ordinary differential equations (ODEs) are mathematical equations that describe how a quantity changes over time or space, given initial conditions. They consist of an unknown function and its derivatives, which are related to each other through a specific differential equation. ODEs are fundamental in modeling dynamic systems across various fields, including physics, biology, and economics, where they help predict the behavior of systems over time. For instance, they can model population growth, chemical reactions, or electrical circuits. Solving ODEs involves finding the function that satisfies the equation and meets given initial conditions, often using analytical methods for simpler cases or numerical techniques for more complex scenarios.
