Solution of Linear Time Invariant Differential Equations with `Proper´ Primitives

The concept of ´proper´ primitives of generalised complex derivatives will be presented. It will be shown, that such ´proper´ primitives can be generated by a functional transformation. Within this framework of proper primitives, linear differential equations containing derivatives of arbitrary order can be solved for any set of n initial conditions, if the solution of the characteristic equation consists of n roots. In difference to the classical case, where a differential equation of the order n has to satisfy n initial conditions for all the derivatives of order 0 to n-1, the choice of the orders of the derivatives subject to initial conditions is arbitrary for proper primitives. This allows to take such initial conditions which are imposed by the context of the given problem. The application of this concept will be demonstrated on simple systems