Mathematical basis of the integral formalism of chemical kinetics. Compact representation of the general solution of the first-order linear differential equation

The standard approach in chemical and photochemical kinetics is to proceed from the kinetic scheme to the corresponding system of first-order differential equations, and then to integrate it, analytically or numerically. An equivalent integral formulation circumventing such system was recently developed on the basis of physical arguments. The mathematical basis of this ansatz is discussed here. A compact representation of the general solution of the linear first-order differential equation is also obtained.