K. NonlaoponS. OrankitjaroenA. KananthaiKhon Kaen UniversityMahidol UniversityChiang Mai University2018-11-232018-11-232015-01-01Integral Transforms and Special Functions. Vol.26, No.12 (2015), 1015-102414768291106524692-s2.0-84941207141https://repository.li.mahidol.ac.th/handle/123456789/36206© 2015 Taylor & Francis. In this paper, we propose the generalized solutions of the differential equation (Formula presented.) where m and n are any integers with (Formula presented.) , and (Formula presented.) 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 (Formula presented.) , 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].Mahidol UniversityMathematicsArticleSCOPUS10.1080/10652469.2015.1079906