Data-driven modelling of non-linear systems with unknown dynamics is a challenging topic. An integral part of this task is the collection of a data set that fully captures the system's behavior in its application scope. The state-of-the-art methods are limited to heuristic input signal generators or model-based optimization methods with strong a priori knowledge assumptions. Currently, there is no approach that simultaneously learns a model, while being end-to-end differentiable w.r.t. a model-independent objective function in order to avoid learning and data set biases. Therefore, the differentiable model predictive excitation (DMPE) algorithm is proposed. The open-sourced, JAXbased algorithm starts with a randomly initialized model that is learnt in parallel to the excitation process from the gathered data. The model is used in a model predictive control fashion in order to maximize the quality of the resulting data set and keep the system within its constraints. The quality of the data set is measured using the Jensen-Shannon divergence based on the joint state-action space. In three numerical application experiments, the algorithm's general applicability and its improved performance in comparison to the current state of the art is demonstrated.