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Deep learning-based garment draping has emerged as a promising alternative to traditional Physics-Based Simulation (PBS), yet robust collision handling remains a critical bottleneck. Most existing methods enforce physical validity through soft penalties, creating an intrinsic trade-off between geometric feasibility and physical plausibility: penalizing collisions often distorts mesh structure, while preserving shape leads to interpenetration. To resolve this conflict, we present PhysDrape, a hybrid neural-physical solver for physically realistic garment draping driven by explicit forces and constraints. Unlike soft-constrained frameworks, PhysDrape integrates neural inference with explicit geometric solvers in a fully differentiable pipeline. Specifically, we propose a Physics-Informed Graph Neural Network conditioned on a physics-enriched graph -- encoding material parameters and body proximity -- to predict residual displacements. Crucially, we integrate a differentiable two-stage solver: first, a learnable Force Solver iteratively resolves unbalanced forces derived from the Saint Venant-Kirchhoff (StVK) model to ensure quasi-static equilibrium; second, a Differentiable Projection strictly enforces collision constraints against the body surface. This differentiable design guarantees physical validity through explicit constraints, while enabling end-to-end learning to optimize the network for physically consistent predictions. Extensive experiments demonstrate that PhysDrape achieves state-of-the-art performance, ensuring negligible interpenetration with significantly lower strain energy compared to existing baselines, achieving superior physical fidelity and robustness in real-time.