This work deals with a study on ordinary differential equations through the presentation of
some of the main analytical methods for solving ordinary differential equations alongside the
exhibition of applications of these equations in everyday problems. With the research question
“What applications and chemical, physical, biological, social sciences, or economic phenomena
motivated the study of certain ordinary differential equations whose analytical methods of
resolution are studied in the curricular component of Ordinary Differential Equations in higher
education?” we arrived, through an exploratory research, at some answers such as: determining
the time of death of a person, determining the half-life of radioactive substances, problems
involving falling bodies, and population dynamics. In the paper, we present in detail some of
these applications found in the literature and also adapted by the author.
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