Ordinary differential equations (ODEs) are mathematical equations that relate a function to its derivatives. They describe how a quantity changes over time or space, making them essential in various fields such as physics, engineering, and biology. An ODE typically involves one independent variable and one dependent variable, allowing for the analysis of dynamic systems. Solving an ODE means finding the function that satisfies the equation. Solutions can be explicit, providing a formula for the function, or implicit, defining the relationship between variables without isolating the function. Techniques for solving ODEs include separation of variables, integrating factors, and numerical methods, each suited for different types of equations.