1. The problem statement, all variables and given/known data Find the solution to the heat equation for the following conditions: 2. Relevant equations 3. The attempt at a solution Not sure. I've only encountered the following scenarios: temperatures of both ends are arbitrary values both ends are insulated (so the first partials with respect to x are both zero) the rod is a circle so the temperatures of both ends and their rate of change are equal. I tried using separation of variables but wasn't sure how to proceed after solving the equation for x.