Linear differential equations

Among differential equations in general, linear differential equations enjoy a special status. This is due to their relative simplicity of study, as well as their frequency of appearance in modeling. What's more, the numerical procedures used to obtain approximate solutions are robust, and not subject to the unpredictable fluctuations inherent in non-linear phenomena.

Since the natural framework for modeling is usually 3-dimensional space, phenomena that depend on spatial coordinates are more likely to be described by partial differential equations. This is why differential equations prefer to describe temporal evolutions, in which the scalar variable is time.

A wealth of literature has been written on this subject, particularly in the 19th century. This article, without going into the more technical points raised by special functions, is content to evoke the most elementary aspects of the theory.