Molecular dynamics (MD) simulations are governed by explicit equations of motion, yet most neural approaches that accelerate or emulate MD rely on simulator-generated trajectories, forces, or energies for training. In this work we ask to what extent can physically meaningful molecular trajectories be recovered from the governing laws. We introduce the Differentiable Newtonian Molecular Solver (DINaMo), a physics-informed neural framework that represents molecular trajectories as differentiable functions of time and is trained exclusively through Newtonian dynamics, conservation laws, and analytic interaction potentials on a given equilibrated initial state. Unlike prior physics-informed MD formulations, DINaMo uses no simulator-generated trajectories, forces, velocities, or energies as supervisory targets. In Lennard--Jones argon systems, the learned trajectories reproduce short-time coordinate, energy, and structural observables, including in a larger and denser liquid-like setting where the radial distribution function is recovered. Although currently limited to short temporal horizons, the results indicate that physically meaningful molecular trajectories can emerge directly from physics-only supervision, supporting the feasibility of trajectory-unsupervised neural solvers for molecular dynamics.

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