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By using the method developed in the paper [G.Pantsulaia, G.Giorgadze, Onsome applications of infinite-dimensional cellular matrices, {\it Georg. Inter.J. Sci. Tech., Nova Science Publishers,} Volume 3, Issue 1 (2011), 107-129], itis obtained a representation in an explicit form of the particular solution ofthe linear non-homogeneous ordinary differential equation of the higher orderwhose coefficients are real-valued simple functions.

On a linear non-homogeneous ordinary differential equation of the higher order whose coefficients are real-valued simple step functions