id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-321	Bujac, Cristina; Schlomiuk, Dana; Vulpe, Nicolae	Cubic differential systems with invariant straight lines of total multiplicity seven and four real distinct infinite singularities	2021	110	.pdf	application/pdf	53541	2891	81	= 2−43−9(X − 2Y )(3X − 4mZ)3(3X − 3Y − 2mZ)2(3Y − 2mZ)2 and hence by Lemma 2.6 we have invariant lines of total multiplicity nine, i.e. we are not in the class of systems with invariant lines of total multiplicity exactly seven. 1.2.2. So considering these conditions as well as the conditions (3.145) and (3.146) we calculate H2 = 8r(1 + r)(2 + 2r + u)3 (1 + u)3(r + u)3∆cf V1V2V3, H ′2 = −8r6(1 + r)(1 + r − u)3 (1 + u)3(r + u)3∆cf V1V2V4, where V1 = h(2r − u)(r + u) +m(u− 2)(1 + u), V2 = hr(r + u)(3 + r + u) +m(1 + u)(1 + 3r + u), V3 = hr(r + u)(2r + 4r2 + 2r3 − u+ 2ru+ 3r2u− 8u2 + 2r2u2 − 4u3 + 3ru3 + u4) +m(1 + u)(r3u− 2r − 4r2 − 2r3 − 3ru− 2r2u− 2u2 + 8r2u2 − 3u3 + 4ru3 − u4), V4 = h(r + u)(2r3 + 2r4 − 2r − 2r2 + u− 7ru− 9r2u− r3u+ u2 − 15ru2 − 10r2u2 − u3 − 8ru3 − u4) +m(1 + u)(2 + 2r − 2r2 − 2r3 − u− 9ru− 7r2u+ r3u− 10u2 − 15ru2 + r2u2 − 8u3 − ru3 − u4).	cache/ejde-321.pdf	txt/ejde-321.txt