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

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