Zhang, Xiang Liouvillian integrability of polynomial differential systems. (English) Zbl 1331.34006 Trans. Am. Math. Soc. 368, No. 1, 607-620 (2016). Reviewer: Maite Grau (Lleida) MSC: 34A05 37C10 34C14 37G05 PDFBibTeX XMLCite \textit{X. Zhang}, Trans. Am. Math. Soc. 368, No. 1, 607--620 (2016; Zbl 1331.34006) Full Text: DOI arXiv
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P. A Maple package to find first order differential invariants of 2ODEs via a Darboux approach. (English) Zbl 1344.34002 Comput. Phys. Commun. 185, No. 1, 307-316 (2014). MSC: 34-04 34C15 PDFBibTeX XMLCite \textit{J. Avellar} et al., Comput. Phys. Commun. 185, No. 1, 307--316 (2014; Zbl 1344.34002) Full Text: DOI
Duarte, L. G. S.; da Mota, L. A. C. P. 3D polynomial dynamical systems with elementary first integrals. (English) Zbl 1184.37059 J. Phys. A, Math. Theor. 43, No. 6, Article ID 065204, 17 p. (2010). MSC: 37K35 34A05 12H05 PDFBibTeX XMLCite \textit{L. G. S. Duarte} and \textit{L. A. C. P. da Mota}, J. Phys. A, Math. Theor. 43, No. 6, Article ID 065204, 17 p. (2010; Zbl 1184.37059) Full Text: DOI
Duarte, L. G. S.; da Mota, L. A. C. P. Finding elementary first integrals for rational second order ordinary differential equations. (English) Zbl 1200.34039 J. Math. Phys. 50, No. 1, 013514, 17 p. (2009). MSC: 34C14 34C20 PDFBibTeX XMLCite \textit{L. G. S. Duarte} and \textit{L. A. C. P. da Mota}, J. Math. Phys. 50, No. 1, 013514, 17 p. (2009; Zbl 1200.34039) Full Text: DOI arXiv
Avellar, J.; Duarte, L. G. S.; Duarte, S. E. S.; da Mota, L. A. C. P. A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations. (English) Zbl 1115.65077 Appl. Math. Comput. 184, No. 1, 2-11 (2007). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L05 34A34 34C15 PDFBibTeX XMLCite \textit{J. Avellar} et al., Appl. Math. Comput. 184, No. 1, 2--11 (2007; Zbl 1115.65077) Full Text: DOI arXiv
Duarte, L. G. S.; Duarte, S. E. S.; Da Mota, L. A. C. P.; Skea, J. E. F. An extension of the Prelle-Singer method and a Maple implementation. (English) Zbl 0994.65082 Comput. Phys. Commun. 144, No. 1, 46-62 (2002). MSC: 65L05 65Y15 34A34 34A26 68W30 PDFBibTeX XMLCite \textit{L. G. S. Duarte} et al., Comput. Phys. Commun. 144, No. 1, 46--62 (2002; Zbl 0994.65082) Full Text: DOI
Duarte, L. G. S.; Duarte, S. E. S.; da Mota, L. A. C. P.; Skea, J. E. F. Solving second-order ordinary differential equations by extending the Prelle-Singer method. (English) Zbl 1017.34010 J. Phys. A, Math. Gen. 34, No. 14, 3015-3024 (2001). Reviewer: Pavol Chocholatý (Bratislava) MSC: 34A45 34A05 PDFBibTeX XMLCite \textit{L. G. S. Duarte} et al., J. Phys. A, Math. Gen. 34, No. 14, 3015--3024 (2001; Zbl 1017.34010) Full Text: DOI
Llibre, Jaume Algebraic solutions and integrability for planar polynomial differential systems. (English) Zbl 0913.34031 García, C. (ed.) et al., Proceedings of the 4th Catalan days on Applied Mathematics, Tarragona, Spain, February 11-13, 1998. Tarragona: Univ., Department d’Enginyeria Informàtica, 81-88 (1998). Reviewer: S.Siegmund (Augsburg) MSC: 34C11 34A05 37G15 PDFBibTeX XMLCite \textit{J. Llibre}, in: Proceedings of the 4th Catalan days on Applied mathematics, Tarragona, Spain, February 11-13, 1998. Tarragona: Univ., Department d'Enginyeria Informàtica. 81--88 (1998; Zbl 0913.34031)
Odani, Kenzi The integration of polynomial Liénard systems by elementary functions. (English) Zbl 0899.34018 Differ. Equ. Dyn. Syst. 5, No. 3-4, 347-354 (1997). Reviewer: T.B.Ward (Norwich) MSC: 34C05 37G15 PDFBibTeX XMLCite \textit{K. Odani}, Differ. Equ. Dyn. Syst. 5, No. 3--4, 347--354 (1997; Zbl 0899.34018)
Man, Yiu-Kwong; MacCallum, Malcolm A. H. A rational approach to the Prelle-Singer algorithm. (English) Zbl 0922.12007 J. Symb. Comput. 24, No. 1, 31-43 (1997). Reviewer: F.Schwarz (Paderborn) MSC: 12H20 12Y05 68W30 34A30 PDFBibTeX XMLCite \textit{Y.-K. Man} and \textit{M. A. H. MacCallum}, J. Symb. Comput. 24, No. 1, 31--43 (1997; Zbl 0922.12007) Full Text: DOI