Short-term origin-destination (OD) demand prediction is critical in managing the multimodal transportation system. The joint short-term OD demand prediction for multimodal systems faces three challenges: (1) data availability: real-time OD demand is not available for prediction; (2) sparsity and high-dimensionality of OD demand: the OD demand is spatiotemporal sparse and usually high dimension; (3) impact of different transportation modes: the future OD demand for one mode is affected by others, and extensive studies primarily focus on a single transportation mode, overlooking the influence between different modes. To tackle these challenges, we propose a multitask learning and Partial-Differential-based model to predict the short-term Multimodal Transport Systems OD demand (PD-MTSOD), which includes (1) an OD demand learner to estimate real-time OD demand, (2) data aggregation with hypergraph attention to capture spatiotemporal features, and (3) OD demand decomposition into self-generated increment, other-modes-generated increment, and real-time OD demand, and use partial-differential-based methods to model intermodal correlations. Extensive tests on Beijing and New York city's multimodal systems show that PD-MTSOD surpasses baseline models. In addition, we prove the benefits of joint considering multiple transportation and explore the correlations of different transportation modes. This paper offers a reliable method for understanding multimodal transportation systems.