Constructing and solving equations – inverse operations

Two inverse operations are considered in this paper: solving a given equation, i.e. finding its solution space, and constructing an equation from a given set, the elements of which being supposed as its solutions, i.e. finding a suitable representation for a given solution space. These equations and representations need not be unique, they may depend on our requirements, e.g. on smoothness or discreteness. These considerations are explained on differential and functional equations. This paper offers a new interpretation of results taken from the area of difference, differential and functional equations.