Abstract
In this paper, we propose the generalized solutions of the differential equation where m and n are any integers with , and using Laplace transform technique. We find that the types of Laplace transformable solutions in the space of right-sided distributions depend on the relationship between m and n. Precisely, we have a distributional solution provided , and a weak solution otherwise. Our work improves the result of Kananthai [The distribution solutions of ordinary differential equation with polynomial coefficients. Southeast Asian Bull Math. 2001;25:129–134].
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