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On the relation between distinct particular solutions of equation

Published online by Cambridge University Press:  14 November 2011

Guan Ke-ying  and
W. N. Everitt
Guan Ke-ying
Affiliation:
Department of Mathematics, The University of Birmingham, Birmingham BT15 2TT, U.K.
W. N. Everitt
Affiliation:
Department of Mathematics, The University of Birmingham, Birmingham BT15 2TT, U.K.
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Synopsis

There exists a relation (1.5) between any n + 2 distinct particular solutions of the differential equation

In this paper, we show that when and only when n = 0, 1 and 2, this relation can be represented by the following form:

provided the form of this relation function Φn depends only on n and is independent of the coefficients of the equation. This result reveals interesting properties of these non-linear differential equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 917 - 926
Copyright
Copyright © Royal Society of Edinburgh 1993

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