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3y = 0",{"_43":199,"_91":97,"_93":200},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":202,"_91":101,"_93":203},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":205,"_91":105,"_93":206},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":192,"_91":208,"_93":209},"E","y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[213],{"_43":214,"_54":215,"_56":216,"_156":157,"_158":217,"_129":218,"_131":218,"_45":219,"_133":216},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_162":220,"_164":165,"_166":221},4,12302,{"_40":223,"_42":41,"_43":224,"_87":225,"_107":237,"_108":238,"_50":239},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[226,229,232,234],{"_43":227,"_91":92,"_93":228},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":230,"_91":97,"_93":231},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":223,"_91":101,"_93":233},"

Verdadeiro, falso, verdadeiro

",{"_43":235,"_91":105,"_93":236},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[213],{"_40":241,"_42":41,"_43":242,"_87":243,"_107":258,"_108":259,"_50":260},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[244,247,250,252,255],{"_43":245,"_91":92,"_93":246},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":248,"_91":97,"_93":249},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":241,"_91":101,"_93":251},"Indeterminado",{"_43":253,"_91":105,"_93":254},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":256,"_91":208,"_93":257},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[213],[213,262,269,279,286,293,294,302,308,313,319,326],{"_43":263,"_54":69,"_56":70,"_156":157,"_158":264,"_129":160,"_131":160,"_45":265,"_133":268},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_162":266,"_164":165,"_166":267},2,11846,"termodinamica-3",{"_43":270,"_54":271,"_56":272,"_156":157,"_158":273,"_129":274,"_131":274,"_45":275,"_133":278},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_162":276,"_164":165,"_166":277},5,30614,"engenharia-mecatronica-1",{"_43":280,"_54":281,"_56":282,"_156":157,"_158":270,"_129":218,"_131":218,"_45":283,"_133":285},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_162":276,"_164":165,"_166":284},25741,"mecanica-3",{"_43":264,"_54":287,"_56":288,"_156":157,"_158":273,"_129":274,"_131":274,"_45":289,"_133":292},"Engenharia Mecânica","engenharia-mecanica",{"_162":290,"_164":165,"_166":291},11,36318,"engenharia-mecanica-2",{"_43":153,"_54":154,"_56":155,"_156":157,"_158":159,"_129":160,"_131":160,"_45":161,"_133":155},{"_43":295,"_54":296,"_56":297,"_156":157,"_158":-5,"_129":298,"_131":298,"_45":299,"_133":297},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_162":300,"_164":165,"_166":301},18,135489,{"_43":303,"_54":69,"_56":70,"_156":157,"_158":214,"_129":304,"_131":304,"_45":305,"_133":307},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_162":165,"_164":165,"_166":306},8597,"termodinamica-5",{"_43":217,"_54":309,"_56":310,"_156":157,"_158":273,"_129":274,"_131":274,"_45":311,"_133":312},"Engenharia de Petróleo","engenharia-de-petroleo",{"_162":276,"_164":165,"_166":221},"engenharia-de-petroleo-1",{"_43":159,"_54":314,"_56":315,"_156":157,"_158":295,"_129":274,"_131":274,"_45":316,"_133":318},"Física","fisica",{"_162":290,"_164":165,"_166":317},13777,"fisica-4",{"_43":273,"_54":320,"_56":321,"_156":157,"_158":-5,"_129":322,"_131":322,"_45":323,"_133":321},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_162":324,"_164":165,"_166":325},29,351586,{"_43":327,"_54":69,"_56":70,"_156":157,"_158":280,"_129":328,"_131":328,"_45":329,"_133":330},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_162":165,"_164":165,"_166":306},"termodinamica-4","tagsTree",[333,337],{"_43":295,"_54":296,"_56":297,"_156":157,"_158":-5,"_129":298,"_131":298,"_45":299,"_133":297,"_168":334},[335],{"_43":159,"_54":314,"_56":315,"_156":157,"_158":295,"_129":274,"_131":274,"_45":316,"_133":318,"_168":336},[152],{"_43":273,"_54":320,"_56":321,"_156":157,"_158":-5,"_129":322,"_131":322,"_45":323,"_133":321,"_168":338},[339,345,349],{"_43":270,"_54":271,"_56":272,"_156":157,"_158":273,"_129":274,"_131":274,"_45":275,"_133":278,"_168":340},[341],{"_43":280,"_54":281,"_56":282,"_156":157,"_158":270,"_129":218,"_131":218,"_45":283,"_133":285,"_168":342},[343],{"_43":327,"_54":69,"_56":70,"_156":157,"_158":280,"_129":328,"_131":328,"_45":329,"_133":330,"_168":344},[],{"_43":264,"_54":287,"_56":288,"_156":157,"_158":273,"_129":274,"_131":274,"_45":289,"_133":292,"_168":346},[347],{"_43":263,"_54":69,"_56":70,"_156":157,"_158":264,"_129":160,"_131":160,"_45":265,"_133":268,"_168":348},[],{"_43":217,"_54":309,"_56":310,"_156":157,"_158":273,"_129":274,"_131":274,"_45":311,"_133":312,"_168":350},[351],{"_43":214,"_54":215,"_56":216,"_156":157,"_158":217,"_129":218,"_131":218,"_45":219,"_133":216,"_168":352},[353],{"_43":303,"_54":69,"_56":70,"_156":157,"_158":214,"_129":304,"_131":304,"_45":305,"_133":307,"_168":354},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários