The method of solving linear differential equations with constant coefficients by using the operator D, which is given in elementary textbooks, was introduced in 1841 by Boole. In spite of the developments summarised below it remains the best method available for certain types of problem. As usually presented it is a tentative process, justified only by substitution in the original equation of the result produced. It is used only to obtain particular integrals, although it can be adapted to deal with complementary functions. This is not done in practice, however, since these can usually be written down directly.