JOINT (MULTIVARIABLE) DIFFERENTIAL EQUATIONS

Abstract

Differential equations, often heralded as the language of change, have
played a pivotal role in mathematical modeling for centuries. While the study of
single-variable differential equations has been instrumental in understanding
various phenomena, the complexity of many real-world systems demands an
extension of these principles. In this article, we embark on an in-depth exploration
of joint or multivariable differential equations—dynamic mathematical entities that
form the backbone of modeling intricate systems with interconnected variables.
We aim to elucidate their profound significance, delve into diverse real-world
applications, and meticulously dissect the nuanced methods employed to navigate
the intricate solutions of these equations.