A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model various physical, chemical, and biological phenomena.
The solution to a differential equation represents the relationship between the variables in the equation and how they change over time. It can also provide information about the behavior of a system or process.
There are various methods for solving differential equations, including separation of variables, substitution, and using integrating factors. The appropriate method depends on the type and complexity of the equation.
The order of a differential equation refers to the highest derivative present in the equation. For example, a first-order differential equation contains only first derivatives, while a second-order equation contains second derivatives.
Differential equations are important in science because they can accurately model and predict the behavior of complex systems and processes. They are used in many fields, including physics, engineering, biology, and economics.