Abstract. This article explores methods of mathematical modeling using differential equations in the certification process of modern technical devices. During certification, the reliability, stability, and functional compliance of devices serve as key criteria. To evaluate these characteristics, differential equations describing physical processes are utilized. The paper presents the problem formulation, introduces fundamental concepts, and, based on lemmas and theorems, demonstrates the existence and uniqueness of the model solution. The obtained results confirm the effectiveness of mathematical models in the evaluation of modern engineering systems.

Keywords: differential equations, mathematical modeling, certification, technical systems, stability, reliability