Here and here it states that water is at its highest density around $4^\circ$ Celsius. I know very little physics and a Google search has left me without an answer. I am teaching an ODE class in the math department. I have a student that heard the above stated in a physics course. She is wondering whether this is an appropriate project for my class. So, does this fact come from some differential equations?
Here is a link which discuses this problem in some depth. I do not think that this would be a good project for an ODE class because temperature and density are not differentially related to each other i.e. one is not a differential form of the other.