Research in quantum machine learning has recently proliferated due to the potential of quantum computing to accelerate machine learning. An area of machine learning that has not yet been explored is neural ordinary differential equation (neural ODE) based residual neural networks (ResNets), which aim to improve the effectiveness of neural networks using the principles of ordinary differential equations. In this work, we present our insights about why analog Rydberg atom quantum computers are especially well-suited for ResNets. We also introduce ResQ, a novel framework to optimize the dynamics of Rydberg atom quantum computers to solve classification problems in machine learning using analog quantum neural ODEs.