A first order differential equation is a mathematical equation that describes the relationship between a function and its derivative. It is represented in the form of dy/dx = f(x,y), where y is the dependent variable and x is the independent variable.
The order of a differential equation is determined by the highest derivative that appears in the equation. A first order differential equation has only one derivative, while a second order differential equation has two derivatives.
The general solution of a first order differential equation is the most general form of the solution that satisfies the equation. It includes an arbitrary constant that can take any value, allowing for an infinite number of specific solutions.
There are several methods for solving first order differential equations, including separation of variables, integrating factors, and substitution. The method used depends on the specific form of the equation.
First order differential equations are used to model a wide range of phenomena in science and engineering, such as population growth, chemical reactions, and electric circuits. They are also used in economics, finance, and biology to make predictions and analyze data.