In recent years, the increasing complexity and diversity of data-based fault detection and isolation (FDI) methods usually require high computational efforts in the pre-processing stage, large amounts of data, and, most of the time, some feature extraction to obtain relevant information for the data-based algorithms. This paper proposes using the Neural Ordinary Differential Equations (NODE) framework to represent the dynamics of the studied plant and later employ such representation in FDI system design. Such an approach enables loss optimization to be performed jointly in the plant dynamics and external inputs without previous use of complex pre-processing and is useful for working with nonlinear systems. The approach is first validated using a simulated Unmanned Aerial Vehicle (UAV) and later applied to a data-set that contains actuators and sensors faults. Ultimately, the proposed approach is compared with other usual machine learning techniques, showing better performance metrics.