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

",[132,150,159,166],{"_19":133,"_56":134,"_135":136,"_137":138,"_139":140,"_68":141,"_70":141,"_64":142,"_148":149},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","alias","engenharia-civil","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_143":144,"_145":106,"_146":147},"childrenCount",21,"content_count","question_count",45865,"slug","engenharia-civil-3",{"_19":151,"_56":152,"_135":153,"_137":138,"_139":133,"_68":154,"_70":154,"_64":155,"_148":158},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_143":156,"_145":106,"_146":157},5,8852,"estruturas-1",{"_19":160,"_56":161,"_135":162,"_137":138,"_139":151,"_68":163,"_70":163,"_64":164,"_148":162},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","Análise Estrutural","analise-estrutural","2025-04-29T04:00:06.9766+00:00",{"_143":106,"_145":106,"_146":165},4694,{"_19":140,"_56":167,"_135":168,"_137":138,"_139":-5,"_68":169,"_70":169,"_64":170,"_148":168},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_143":171,"_145":106,"_146":172},29,351586,{"_16":17,"_18":17,"_19":174,"_21":175,"_45":17,"_46":188,"_88":189},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[176,179,182,185],{"_19":177,"_25":26,"_27":178},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":180,"_25":31,"_27":181},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":183,"_25":35,"_27":184},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":186,"_25":39,"_27":187},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[132,150,159,166],{"_16":17,"_18":17,"_19":191,"_21":192,"_45":17,"_46":205,"_88":206},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[193,196,199,202],{"_19":194,"_25":26,"_27":195},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":197,"_25":31,"_27":198},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":200,"_25":35,"_27":201},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":203,"_25":39,"_27":204},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[132,150,159,166],{"_16":17,"_18":17,"_19":208,"_21":209,"_45":17,"_46":225,"_88":226},"996628fc-4ac3-4821-86bd-839f86a97a6d",[210,213,216,219,222],{"_19":211,"_25":26,"_27":212},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":214,"_25":31,"_27":215},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":217,"_25":35,"_27":218},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":220,"_25":39,"_27":221},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":223,"_25":43,"_27":224},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[132,150,159,166],{"_16":17,"_18":17,"_19":228,"_21":229,"_45":17,"_46":245,"_88":246},"c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,239,242],{"_19":231,"_25":26,"_27":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":234,"_25":31,"_27":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":237,"_25":35,"_27":238},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":240,"_25":39,"_27":241},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":243,"_25":43,"_27":244},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","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????",[132,150,159,166],[132,150,159,166],"tagsTree",[250],{"_19":140,"_56":167,"_135":168,"_137":138,"_139":-5,"_68":169,"_70":169,"_64":170,"_148":168,"_251":252},"children",[253],{"_19":133,"_56":134,"_135":136,"_137":138,"_139":140,"_68":141,"_70":141,"_64":142,"_148":149,"_251":254},[255],{"_19":151,"_56":152,"_135":153,"_137":138,"_139":133,"_68":154,"_70":154,"_64":155,"_148":158,"_251":256},[257],{"_19":160,"_56":161,"_135":162,"_137":138,"_139":151,"_68":163,"_70":163,"_64":164,"_148":162,"_251":258},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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