In this chapter, a neural dynamics model is constructed and investigated for solving time-dependent Sylvester equations with matrix inversion involved in the solving process. Besides, to eliminate the matrix inversion in the model, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is leveraged to construct a new model. Moreover, the global convergence performance and the effectiveness of the two discrete computational models are testified by providing theoretical analyses and numerical experiments with comparisons to the existing solutions, respectively. Two applications to robotics and the multiple-input multiple-output (MIMO) system are given to elucidate the feasibility of the presented models for solving time-dependent Sylvester equations.