In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics, mixing problems and reactors design, among others. The discussion in this paper will deal with important issues such as existence, uniqueness and stability for mixing problems in relation to teaching experiences. Conclusions based on the results of the teaching methods used, will be drawn for differential equations courses and other mathematical service courses. (Contains 1 figure and 3 tables.)