On the sustainability of individually weighted decisions simple differential equations

The paper investigates the solution of nonlinear singularly perturbed ordinary differential equations. The eigenvalues of the Jordan matrix determine different types of stability. These types of stability include two-way stability and stability. If there is a two-sided stable domain, then solutions of linear singularly perturbed ordinary differential equations are evaluated in the real domain. Accordingly, there are two-way stable lines that we will apply when choosing the integration path. If the eigenvalues of a Jordan matrix consist of purely imaginary parts, then these eigenvalues generate a biostable region in the plane. The scientific novelty lies in the fact that these types of resistance have been discovered in the course of research, and previously published papers have not been considered. As a result, the theorem is proved and an estimate of solutions of nonlinear singularly perturbed ordinary differential equations is obtained.