{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T06:04:40Z","timestamp":1672812280904},"reference-count":7,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[2003,9]]},"abstract":"\n Most work on finding elementary function solutions for differential equations focussed on linear equations [4, 2, 6, 1, 3]. In this paper, we try to find polynomial solutions to non-linear differential equations. Instead of finding arbitrary polynomial solutions, we will find the polynomial general solutions. For example, the general solution for (d\n y<\/jats:italic>\n \/d\n x<\/jats:italic>\n )\n 2<\/jats:sup>\n - 4\n y<\/jats:italic>\n = 0 is\n y<\/jats:italic>\n = (\n x + c<\/jats:italic>\n )\n 2<\/jats:sup>\n , where\n c<\/jats:italic>\n is an arbitrary constant. We give a necessary and sufficient condition for an ODE with constant coefficients to have polynomial general solutions. For a first order ODE of degree\n n<\/jats:italic>\n and with constant coefficients, we give an algorithm of complexity\n O<\/jats:italic>\n (\n n<\/jats:italic>\n 9<\/jats:sup>\n ) to decide if it has a polynomial general solution and to compute the solution if it exists.\n <\/jats:p>","DOI":"10.1145\/990353.990360","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"71-72","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Polynomial solutions for first order ODEs with constant coefficients"],"prefix":"10.1145","volume":"37","author":[{"given":"Ruyong","family":"Feng","sequence":"first","affiliation":[{"name":"Institute of System Science, Academia Sinica, Beijing, China"}]},{"given":"Xiao-Shan","family":"Gao","sequence":"additional","affiliation":[{"name":"Institute of System Science, Academia Sinica, Beijing, China"}]}],"member":"320","published-online":{"date-parts":[[2003,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80106-X"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(86)80010-4"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2001.0461"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0237477-8"},{"key":"e_1_2_1_5_1","volume-title":"Differential algebra","author":"Ritt J. F.","year":"1950","unstructured":"J. F. Ritt , Differential algebra , Amer. Math. Sco. Colloquium, New York , 1950 . J. F. Ritt, Differential algebra, Amer. Math. Sco. Colloquium, New York, 1950."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80048-X"},{"key":"e_1_2_1_7_1","volume-title":"Mathematics mechanization","author":"Wu W. T.","year":"2000","unstructured":"W. T. Wu , Mathematics mechanization , Science Press\/Kluwer , Beijing , 2000 . W. T. Wu, Mathematics mechanization, Science Press\/Kluwer, Beijing, 2000."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/990353.990360","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T11:30:29Z","timestamp":1672745429000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/990353.990360"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,9]]}},"alternative-id":["10.1145\/990353.990360"],"URL":"https:\/\/doi.org\/10.1145\/990353.990360","relation":{},"ISSN":["0163-5824"],"issn-type":[{"value":"0163-5824","type":"print"}],"subject":[],"published":{"date-parts":[[2003,9]]},"assertion":[{"value":"2003-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}
