INTUITION for ordinary differential equations largely stems from the time evolution ofphysical systems. Equations like Newton’s second law, determining the motion of physical objects over time, dominate the literature on ODE problems; additional examples come from chemical concentrations reacting over time, populations of predators and prey interacting from season to season, and so on. In each case, the initial configuration-e.g., the positions and velocities of particles in a system at time zero-is known, and the task is to predict behavior as time progresses. Derivatives only appear in a single time variable.