{"title":"Elementary first integrals of differential equations","authors":"M. J. Prelle, M. Singer","doi":"10.1145/800206.806368","DOIUrl":null,"url":null,"abstract":"It is not always possible and sometimes not even advantageous to write the solutions of a system of differential equations explicitly in terms of elementary functions. Sometimes, though, it is possible to find elementary functions which are constant on solution curves, that is, elementary first integrals. These first integrals allow one to occasionally deduce properties that an explicit solution would not necessarily reveal.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1981-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"307","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Symbolic and Algebraic Manipulation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800206.806368","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 307
Abstract
It is not always possible and sometimes not even advantageous to write the solutions of a system of differential equations explicitly in terms of elementary functions. Sometimes, though, it is possible to find elementary functions which are constant on solution curves, that is, elementary first integrals. These first integrals allow one to occasionally deduce properties that an explicit solution would not necessarily reveal.
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