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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Liouvillian solutions of the differential equation $ y''+S(x)y=0$ with $ S(x)$ binomial


Author: Minoru Setoyanagi
Journal: Proc. Amer. Math. Soc. 100 (1987), 607-612
MSC: Primary 34C20; Secondary 34A10, 34A30
MathSciNet review: 894424
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Abstract: If a differential equation $ y'' + (a{x^p} + b{x^q})y = 0$ with $ p > q$ has a liouvillian solution, then $ p$ is an even number $ 2m$ and the number $ s = (m + 1)/(p - q)$ is an integer. The case $ s = 2$ occurs only if $ m = 1$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0894424-X
PII: S 0002-9939(1987)0894424-X
Article copyright: © Copyright 1987 American Mathematical Society