On the integrability of differential equations by quadratures according to Maximovič

Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2004. On the integrability of differential equations by quadratures according to Maximovič. Journal of Computational and Applied Mathematics 171 (1-2) , pp. 393-410. 10.1016/j.cam.2004.01.021

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Abstract

We show that a first-order ordinary differential equation can be integrated by quadratures in the sense of Maximovič only if it arises from the linear equation by a diffeomorphic transformation of the dependent variable. In the appendix this result is applied to show that the linear second-order equation can be integrated by quadratures in a restricted sense only if it has constant coefficients. A brief outline of Maximovič's life is also included.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Differential equations; Integration by quadratures
Publisher:	Elsevier
ISSN:	0377-0427
Last Modified:	18 Oct 2022 13:15
URI:	https://orca.cardiff.ac.uk/id/eprint/13239

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