Artificial neural networks are a relatively new approach to data processing. Deep models have been shown to have a greater ability to learn information from data than other machine learning models. Convolution, residual and recurrent neural networks have been developed. Neural networks are optimized to minimize the loss function but still retain the ability to generalize. Continuous-depth neural networks have also been developed. They are also called neural ordinary differential equations. This approach to neural networks significantly reduces the number of parameters that need to be optimized and the depth is not defined the same way as in other neural networks. This family of ordinary differential equations, instead of a discrete set of hidden layers, has a parameterized derivation of the hidden state using a neural network. The output of such a network is calculated using a black box differential equation solver. Training such a neural network using conventional training methods is computationally demanding, so the adjoint method for calculating network gradients is applied. Applying the neural ordinary differential equation to the online available MNIST dataset provides encouraging results. Also, in a simple example such as a simple spiral, this network produces better results compared to the previously known neural networks.