In this work, we investigate the capabilities of the DeepXDE library to solve mathematical models based on ordinary and partial differential equations using Physics-Informed Neural Networks (PINNs). PINNs are an important machine learning tool for solving complex problems modeled by differential equations, by incorporating physical laws into the neural network structure. We assess the versatility and effectiveness of DeepXDE by applying the PINNs methodology to several initial and boundary value problems, including the Verhulst logistic model, the 1D Gray-Scott reaction-diffusion system, the SIR epidemiological model, the incompressible Navier-Stokes equations, and an inverse problem derived from epidemiological data. The DeepXDE library facilitates the implementation of PINNs by providing an efficient and easy-to-use tool both for educational purposes (classroom use) and for solving direct and inverse problems in engineering and computational science.