English

On the integrability in finite terms of first-order differential equations according to Maximovic

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We give a definition of integration by quadratures of first-order ordinary differential equations, and recover a little known result by Maximovic which states that a first-order ordinary differential equation can be integrated by quadratures only if it arises from the linear equation by a diffeomorphic transformation of the dependent variable. In the appendix this result is applied to the linear second-order equation in a restricted setting. A brief outline of Maximovic's life is also included.

Keywords

Cite

@article{arxiv.math/9906013,
  title  = {On the integrability in finite terms of first-order differential equations according to Maximovic},
  author = {Karl Michael Schmidt},
  journal= {arXiv preprint arXiv:math/9906013},
  year   = {2007}
}

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24 pages