ordinary differential equations

Ordinary Differential Equations (ODEs) are mathematical equations that describe the relationship between a function and its derivatives. They capture how things change over time or space, such as how populations grow, how vehicles move, or how heat spreads. An ODE can help predict future behaviors based on current conditions and rules governing the system. Solving an ODE involves finding a function that satisfies the equation, providing insights into various natural and engineered processes. Overall, ODEs are essential tools in fields ranging from physics and engineering to biology and economics, facilitating understanding of dynamic systems.