River network routing is a crucial component of watershed hydrological modeling, with the Muskingum method being one of the most widely used approaches. However, traditional applications of the Muskingum method typically rely on discrete difference equations, which not only introduce numerical errors but also hinder seamless temporal-scale coupling with hydrological models formulated in differential form. To address this limitation, this study develops a differential form of the Muskingum river routing method by assembling the governing ordinary differential equations (ODEs) for all river segments using a matrix-based approach. A connectivity matrix is introduced to identify upstream inflows for each channel, leading to the formulation of the Muskingum-based Ordinary Differential Equation River-network Routing method (ODE-MR). The ODE-MR is further coupled with the differential form of the Xinanjiang hydrological model to construct a fully differential hydrological modeling framework.Comparative experiments between differential and difference forms demonstrate that, with analytical solutions as reference, the root mean square error of ODE-MR is on the order of 10??, significantly reducing the numerical inaccuracies of the traditional difference-based Muskingum method. Additional experiments comparing the coupling strategies with differential hydrological models show that, as the time step decreases, the results of the hybrid differential-difference coupling approach gradually converge toward those of the fully differential coupling method, indicating superior modeling accuracy of the fully differential coupling method approach. Real-world application in the Tunxi River Basin further validates the model, at the daily scale, with the ODE-MR-based fully differential coupling model improving the multi-year average Nash-Sutcliffe efficiency coefficient by 0.04, demonstrating enhanced predictive performance. This study provides a valuable reference for hydrological modeling and cross-disciplinary model integration within a unified differential equation framework.