Discovering Ordinary Differential Equations (ODEs) from trajectory data is a critical task in AI-driven scientific discovery. Recent methods for symbolic discovery of ODEs primarily rely on fixed training datasets collected a priori. How- ever, it often results in suboptimal performance, as shown in our observations in Figure 1. Inspired by the active learning strategy, we consider querying informative trajectory data to evaluate predicted ODEs. Chaos theory suggests that small changes in the initial conditions of a dynamical system can lead to vastly different trajectories, which ask for maintaining a large set of initial conditions. To address this challenge, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Rather than directly selecting individual initial conditions, APPS first identifies an informative region and then samples a batch of initial conditions within that region. Compared to traditional active learning methods, APPS eliminates the need to maintain large amounts of training data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions compared to baseline methods. Furthermore, APPS achieves superior performance while significantly reducing the amount of data and training time required