The use of neural networks in embedded systems is becoming increasingly common, but these systems often operate in safety–critical environments, where a failure or incorrect output can have serious consequences. Therefore, it is essential to verify the expected operation of neural networks before deploying them in such settings. In this publication, we present a novel approach for verifying the correctness of these networks using a nonlinear equation system under the assumption of closed-form activation functions. Our method is able to accurately predict the output of the network for given specification intervals, providing a valuable tool for ensuring the reliability and safety of neural networks in embedded systems.