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On the integrability of differential equations by quadratures according to Maximovič

Schmidt, Karl Michael 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: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Differential equations; Integration by quadratures
Publisher: Elsevier
ISSN: 0377-0427
Last Modified: 04 Jun 2017 04:24
URI: http://orca.cf.ac.uk/id/eprint/13239

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