Ten life lessons from differential equations:

— Some problems simply have no solution.

— Some problems have no simple solution.

— Some problems have many solutions.

— Determining that a solution exists may be half the work of finding it.

— Solutions that work well locally may blow up when extended too far.

— Boundary conditions are the hard part.

— Something that starts out as a good solution may become a very bad solution.

— You can fool yourself by constructing a solution where one doesn’t exist.

— Expand your possibilities to find a solution, then reduce them to see how good the solution is.

— You can sometimes do what sounds impossible by reframing your problem.