APPLICATION OF THE BERNOULLI DIFFERENTIAL EQUATION IN SOLVING DIFFERENTIAL EQUATIONS

Abstract

The Bernoulli differential equation represents an important class of nonlinear first-order differential equations that can be transformed into linear equations through an appropriate substitution. This property makes it a powerful analytical tool in solving a wide range of differential equations arising in mathematics, physics, engineering, and applied sciences. The present study investigates the application of the Bernoulli equation in solving differential equations and develops a systematic approach for its use. The theoretical foundation of the Bernoulli method, its transformation mechanism, and its structural properties are analyzed in detail. Special attention is given to the conditions under which nonlinear equations can be reduced to linear form and solved using integrating factor techniques. The study also includes a detailed example illustrating the step-by-step solution procedure. The results demonstrate that the Bernoulli equation serves as an effective bridge between linear and nonlinear differential equations and provides a valuable method for solving complex mathematical problems.