Real linear quaternionic operators

In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear second order differential equations with constant coefficients. In this paper, we extend our discussion to real linear quaternionic differential equations. The method of resolution is based on the Jordan canonical form of quaternionic matrices associoated to real linear differential operators.