TITLE: Which solution does a particle follow if uniqueness fails in ODE?
QUESTION [5 upvotes]: If there are multiple solutions to an ODE at y(0) = 0 and a particle is "dropped" into the flow field where the solutions intersect,which path does the particle take?  In other words, which solution do we follow if we start at (0,0)?

REPLY [2 votes]: The particle is real, the ODE is a model. Models are good as far as they go, but should not be confused with reality. If a model doesn't tell you what a particle does, it's a sign that (for the particular questions you ask) you need a better model. For that matter, $(0,0)$ is a model --- there is no $(0,0)$ in the real world.