Integration of an arbitrary linear ODE

The standard text book theory of ODEs lacks a general method to solve linear equations having variable coefficients, providing instead a collection of special techniques for particular classes of equations. The present article addresses this shortcoming in the basic theory. We introduce the multex integral operator, generalizing to several input functions the standard exponential primitive operator that is inverse to the logarithmic derivative. The multex operator serves to integrate in explicit form an arbitrary linear ordinary differential equation.