{"title":"Radical solutions of first order autonomous algebraic ordinary differential equations","authors":"Georg Grasegger","doi":"10.1145/2608628.2608636","DOIUrl":null,"url":null,"abstract":"We present a procedure for solving autonomous algebraic ordinary differential equations (AODEs) of first order. This method covers the known case of rational solutions and depends crucially on the use of radical parametrizations for algebraic curves. We can prove that certain classes of AODEs permit a radical solution, which can be determined algorithmically. However, this approach is not limited to rational and radical solutions of AODEs.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2608628.2608636","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
We present a procedure for solving autonomous algebraic ordinary differential equations (AODEs) of first order. This method covers the known case of rational solutions and depends crucially on the use of radical parametrizations for algebraic curves. We can prove that certain classes of AODEs permit a radical solution, which can be determined algorithmically. However, this approach is not limited to rational and radical solutions of AODEs.
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