> The most important skill in this area is ability to compose differential equation from the description of the problem. This is called "modeling", and togeth

> The most important skill in this area is ability to compose differential equation from the description of the problem. This is called "modeling", and together with analysis and simulation is one of the three main parts of the theory. Where did you study differential equations? From my experience, it is typically taught that way, at least in the european universities that I know. Even in the most hard-core mathematics departments they may focus strongly on the analysis part (existence, uniqueness, regularity) to the detriment of a bit of modeling or simulation; but I have never seen those hidden. The "algebraic" solution of the equations is a fringe subject that is most often omitted, (except when it leads to a simple analysis, e.g. linear equations).