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3y = 0",{"_43":212,"_84":90,"_86":213},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":215,"_84":94,"_86":216},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":218,"_84":98,"_86":219},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":205,"_84":102,"_86":221},"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

",[225],{"_43":226,"_54":227,"_56":228,"_153":154,"_155":229,"_126":230,"_128":230,"_45":231,"_130":228},"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",{"_158":232,"_160":161,"_162":233},4,12302,{"_40":235,"_42":41,"_43":236,"_80":237,"_104":249,"_105":250,"_50":251},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[238,241,244,246],{"_43":239,"_84":85,"_86":240},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":242,"_84":90,"_86":243},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":235,"_84":94,"_86":245},"

Verdadeiro, falso, verdadeiro

",{"_43":247,"_84":98,"_86":248},"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?

",[225],{"_40":253,"_42":41,"_43":254,"_80":255,"_104":270,"_105":271,"_50":272},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[256,259,262,264,267],{"_43":257,"_84":85,"_86":258},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":260,"_84":90,"_86":261},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":253,"_84":94,"_86":263},"Indeterminado",{"_43":265,"_84":98,"_86":266},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":268,"_84":102,"_86":269},"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????",[225],[225,274,283,289,293,294,295,303,308,316,317,322,328],{"_43":275,"_54":276,"_56":277,"_153":154,"_155":278,"_126":170,"_128":170,"_45":279,"_130":282},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_158":280,"_160":161,"_162":281},5,30614,"engenharia-mecatronica-1",{"_43":284,"_54":62,"_56":63,"_153":154,"_155":285,"_126":286,"_128":286,"_45":287,"_130":288},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-6",{"_43":285,"_54":168,"_56":169,"_153":154,"_155":275,"_126":230,"_128":230,"_45":290,"_130":292},{"_158":280,"_160":161,"_162":291},25741,"mecanica-3",{"_43":150,"_54":151,"_56":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_45":157,"_130":152},{"_43":177,"_54":62,"_56":63,"_153":154,"_155":167,"_126":178,"_128":178,"_45":179,"_130":181},{"_43":296,"_54":297,"_56":298,"_153":154,"_155":278,"_126":170,"_128":170,"_45":299,"_130":302},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_158":300,"_160":161,"_162":301},21,45865,"engenharia-civil-3",{"_43":229,"_54":304,"_56":305,"_153":154,"_155":278,"_126":170,"_128":170,"_45":306,"_130":307},"Engenharia de Petróleo","engenharia-de-petroleo",{"_158":280,"_160":161,"_162":233},"engenharia-de-petroleo-1",{"_43":309,"_54":310,"_56":311,"_153":154,"_155":296,"_126":312,"_128":312,"_45":313,"_130":315},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_158":280,"_160":161,"_162":314},8852,"estruturas-1",{"_43":167,"_54":168,"_56":169,"_153":154,"_155":150,"_126":170,"_128":170,"_45":171,"_130":174},{"_43":318,"_54":62,"_56":63,"_153":154,"_155":226,"_126":319,"_128":319,"_45":320,"_130":321},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-7",{"_43":323,"_54":324,"_56":63,"_153":154,"_155":309,"_126":325,"_128":325,"_45":326,"_130":327},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-5",{"_43":278,"_54":329,"_56":330,"_153":154,"_155":-5,"_126":331,"_128":331,"_45":332,"_130":330},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_158":333,"_160":161,"_162":334},29,351586,"tagsTree",[149,337],{"_43":278,"_54":329,"_56":330,"_153":154,"_155":-5,"_126":331,"_128":331,"_45":332,"_130":330,"_164":338},[339,345,351],{"_43":275,"_54":276,"_56":277,"_153":154,"_155":278,"_126":170,"_128":170,"_45":279,"_130":282,"_164":340},[341],{"_43":285,"_54":168,"_56":169,"_153":154,"_155":275,"_126":230,"_128":230,"_45":290,"_130":292,"_164":342},[343],{"_43":284,"_54":62,"_56":63,"_153":154,"_155":285,"_126":286,"_128":286,"_45":287,"_130":288,"_164":344},[],{"_43":296,"_54":297,"_56":298,"_153":154,"_155":278,"_126":170,"_128":170,"_45":299,"_130":302,"_164":346},[347],{"_43":309,"_54":310,"_56":311,"_153":154,"_155":296,"_126":312,"_128":312,"_45":313,"_130":315,"_164":348},[349],{"_43":323,"_54":324,"_56":63,"_153":154,"_155":309,"_126":325,"_128":325,"_45":326,"_130":327,"_164":350},[],{"_43":229,"_54":304,"_56":305,"_153":154,"_155":278,"_126":170,"_128":170,"_45":306,"_130":307,"_164":352},[353],{"_43":226,"_54":227,"_56":228,"_153":154,"_155":229,"_126":230,"_128":230,"_45":231,"_130":228,"_164":354},[355],{"_43":318,"_54":62,"_56":63,"_153":154,"_155":226,"_126":319,"_128":319,"_45":320,"_130":321,"_164":356},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários