A large number of embedded computing systems are modeled as hybrid system with both discrete and continuous dynamics. In this paper, we present algorithms for analyzing nonlinear time-invariant continuous-time systems by employing reachability algorithms. We propose synthesis algorithms for finding sets of initial states for the continuous dynamical systems so that temporal properties, such as safety and liveness properties, are satisfied. The initial sets produced by the algorithms are related to some classical concepts for continuous dynamical systems, such as invariant sets and domains of attraction.