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We aim to teach robots to perform simple object manipulation tasks by watching a single video demonstration. Towards this goal, we propose an optimization approach that outputs a coarse and temporally evolving 3D scene to mimic the action demonstrated in the input video. Similar to previous work, a differentiable renderer ensures perceptual fidelity between the 3D scene and the 2D video. Our key novelty lies in the inclusion of a differentiable approach to solve a set of Ordinary Differential Equations (ODEs) that allows us to approximately model laws of physics such as gravity, friction, and hand-object or object-object interactions. This not only enables us to dramatically improve the quality of estimated hand and object states, but also produces physically admissible trajectories that can be directly translated to a robot without the need for costly reinforcement learning. We evaluate our approach on a 3D reconstruction task that consists of 54 video demonstrations sourced from 9 actions such as pull something from right to left or put something in front of something. Our approach improves over previous state-of-the-art by almost 30%, demonstrating superior quality on especially challenging actions involving physical interactions of two objects such as put something onto something. Finally, we showcase the learned skills on a Franka Emika Panda robot.