  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.
