Abstract
The Kummer–Schwarz Equation, 2<em>y'y'''</em>− 3(<em>y''</em>)<sup>2</sup> = 0, has a generalisation, (<em>n</em> − 1)<em>y</em><sup>(<em>n</em>−2)</sup><em>y</em><sup>(<em>n</em>)</sup> − <em>ny</em><sup>(<em>n</em>−1)<sup>2</sup></sup> = 0, which shares many properties with the parent form in terms of symmetry and singularity. All equations of the class are integrable in closed form. Here we introduce a new class, (<em>n</em>+q−2)<em>y</em><sup>(<em>n</em>−2</sup>)<em>y</em><sup>(<em>n</em>)</sup> −(<em>n</em>+<em>q</em>−1)<em>y</em><sup>(<em>n</em>−1)<sup>2</sup></sup> = 0, which has different integrability and singularity properties.
Publisher
Czech Technical University in Prague - Central Library
Cited by
1 articles.
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