The monotonic stability of the implicit differential equations system solution on an infinite interval

The non-stationary system of two ordinary differential equations in implicit first-order form is considered. The aim of the article is to describe the method of monotonic stability analysis (MSA) of solving the equations of a given system with respect to a resting point. When studying the stability of solutions, elements of mathematical analysis of functions of one variable are applied. The work formulates the monotonic stability sufficient condition of partial solutions of partial solutions on an infinite interval, as well as a theorem of the tendency of the monotonically stable solution to an asymptotically stable rest point. The presented theorems are considered with their proofs. A comparison is made of method of the MSA and Lyapunov's method. The application of the obtained method is presented by the example of the MS analysis of the partial solutions of a dynamical system tending to a resting point in the form of a stable diacritic node.