This paper presents the topic of first-order ordinary differential equations and their applications, discussing a little about the history of the emergence of differential equations, their main characteristics and some methods for solving a first-order linear equation, mainly for solving initial value problems, among them the method for obtaining the solution of linear equations using, especially, the integrating factor, the method for obtaining the solution of separable equations, the method for obtaining the solution of homogeneous equations and the method for obtaining the solution of exact equations. A method is also used to reduce the order of a higher-order differential equation to a first-order linear equation in order to obtain its solution and finally the method for obtaining the solution of Bernoulli equations is presented. With the presentation of the methods, it is possible to guarantee that this solution exists and is unique through the existence and uniqueness theorems. With this, these presented methods can be used for applications in problems, often used by other sciences.
|
