{"title":"一阶自治代数常微分方程的根解","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":"{\"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}","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}
Radical solutions of first order autonomous algebraic ordinary differential equations
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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