METHOD FOR SOLVING EXACT DIFFERENTIAL EQUATIONS

Abstract

Exact differential equations constitute an important class of first-order differential equations widely used in mathematical analysis, physics, engineering, and applied sciences. These equations possess a special structure that allows them to be solved through the identification of a potential function whose total differential coincides with the given equation. The present study examines the theoretical foundations of exact differential equations and develops a systematic method for constructing their general solutions. Particular attention is given to the mathematical conditions under which a differential equation is exact and to the algorithm used for determining the potential function. The work analyzes the structural properties of exact equations and demonstrates the solution procedure through a detailed example. The results show that the method of exact equations provides an effective analytical tool for solving certain classes of nonlinear differential equations and contributes to a deeper understanding of differential relationships between variables.