
Published online:
01 May 2008
Published in print:
07 February 2008
Online ISBN:
9780191715853
Print ISBN:
9780199535286
Contents
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3.1 A class of autonomous ODEs 3.1 A class of autonomous ODEs
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3.2 Examples 3.2 Examples
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3.2.1 First-order algebraic complex ODE 3.2.1 First-order algebraic complex ODE
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3.2.2 Polynomial vector field in the plane 3.2.2 Polynomial vector field in the plane
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3.2.3 Oscillator with additional inverse-cube force 3.2.3 Oscillator with additional inverse-cube force
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3.2.4 Isochronous versions of the first and second Painlevé ODEs (complex and real versions) 3.2.4 Isochronous versions of the first and second Painlevé ODEs (complex and real versions)
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3.2.5 Autonomous second-order ODEs (complex and real versions) 3.2.5 Autonomous second-order ODEs (complex and real versions)
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3.2.6 Autonomous third-order ODEs (complex and real versions) 3.2.6 Autonomous third-order ODEs (complex and real versions)
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3.2.7 Isochronous version of a solvable second-order ODE due to Painlev 3.2.7 Isochronous version of a solvable second-order ODE due to Painlev
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3.2.8 Isochronous versions of five solvable ODEs due to Chazy 3.2.8 Isochronous versions of five solvable ODEs due to Chazy
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3.N Notes to Chapter 3 3.N Notes to Chapter 3
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Chapter
3 A SINGLE ODE OF ARBITRARY ORDER
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Pages
23–50
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Published:February 2008
Cite
Calogero, Francesco, 'A SINGLE ODE OF ARBITRARY ORDER', Isochronous Systems (Oxford , 2008; online edn, Oxford Academic, 1 May 2008), https://doi.org/10.1093/acprof:oso/9780199535286.003.0003, accessed 15 May 2025.
Abstract
In Chapter 3 several ω-modified ordinary differential equations (ODEs) are obtained and their isochronous character is discussed. Firstly a large class of such equations is identified and several of the cases it includes are discussed. The ω-modified, isochronous versions of several classical ODEs are then treated, including first-order algebraic ODEs, the ODEs describing a polynomial vector field in the plane, the ODE of a standard oscillator with an additional cubic force, the first Painlevé ODE, other second- and third-order ODEs, and certain interesting ODEs introduced by Painlevé and by Chazy.
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