The longitudinal analysis of patient response time course following doses of therapeutics is currently performed using Pharmacokinetic/Pharmacodynamic (PK/PD) methodologies, which requires significant human experience and expertise in the modeling of dynamical systems. By utilizing recent advancements in deep learning, we show that the governing differential equations can be learnt directly from longitudinal patient data. In particular, we propose a novel neural-PK/PD framework that combines key pharmacological principles with neural ordinary differential equations. We applied it to an analysis of drug concentration and platelet response from a clinical dataset consisting of over 600 patients. We show that the neural-PK/PD model improves upon a state-of-the-art model with respect to metrics for temporal prediction. Furthermore, by incorporating key PK/PD concepts into its architecture, the model can generalize and enable the simulations of patient responses to untested dosing regimens. These results demonstrate the potential of neural-PK/PD for automated predictive analytics of patient response time course.