SILVA, Vandermir Santos.
Abstract:
This work presents a study on ordinary differential equations, where initially
a little about the emergence and study of these equations is presented, as well as
the leading names that gave their contributions to their development. Bibliographic
research was carried out on first and second-order ordinary differential equations, where
we present their main definitions: classification as to type, order, and linearity, the
existence of solution, initial value problems, and the main methods to find solutions
for these types of equations. As an application, we did a study on Newton’s Law of
Cooling and presented a problem with application in criminal expertise. We also work
with the spring-mass system modeled through a second-order differential equation,
focusing on the damped mass-spring system. We present a problem that involves the
three possible types of the damped motion: super damped, critically damped, and
undamped. We then realized the importance of studying Differential Equations not
only for mathematics but also for other areas of knowledge, since it allows modeling
different situations studied by these areas.
