1. General results

1.1 Problem position

A differential equation is said to be linear when it expresses the cancellation condition of a linear application, or, if you prefer, of a differential operator. In contrast to partial differential equations, differential equations have functions of a single scalar variable as their unknown functions. We'll concentrate on the case where the variable is real. If E is a normed vector space, the space of continuous endomorphisms of E is ${\mathcal{L}}_c\left(E\right)$ .