Note on the Application of Divergent Series for Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

There are many methods for finding a particular solution to a nonhomogeneous linear ordinary differential equation (ODE) with constant coefficients. The method of undetermined coefficients, Laplace transform method and differential operator method are generally known. The latter mentioned method sometimes uses the Maclaurin expansion of an inverse differential operator but only in the case when the obtained series is convergent. The present work deals also with how to find a particular solution if the corresponding infinite series is divergent, using only the terms of that series and the method of summation of divergent series.