A first order differential equation is an equation that involves an unknown function and its derivative with respect to a single independent variable. It can be written in the form dy/dx = f(x), where y is the unknown function and f(x) is a known function of x.
An ordinary first order differential equation involves a single independent variable, while a partial first order differential equation involves multiple independent variables. In other words, an ordinary differential equation describes a relationship between a single variable and its derivative, while a partial differential equation describes a relationship between multiple variables and their partial derivatives.
The order of a first order differential equation refers to the highest derivative present in the equation. Since a first order differential equation only involves the first derivative, its order is 1.
There are several methods for solving a first order differential equation, including separation of variables, integrating factors, and the method of undetermined coefficients. The appropriate method to use depends on the specific form of the equation.
First order differential equations are used to model a variety of real-world phenomena, such as population growth, radioactive decay, and electrical circuits. They are also commonly used in fields such as physics, engineering, economics, and biology.