To solve a differential equation, modern numerical methods are used: Runge-Kutta, finite element method, finite difference method. These methods provide good accuracy, but they work for a long time with large dimensions. This article discusses a neural network of direct distribution, consisting of three layers. To minimize the error function and determine the weights, the backpropagation method is used. The initial weights are taken arbitrarily. Also in the article is determined by the number of elements in the hidden layer of the neural network. The results of the neural network are compared with the results of the Euler method.