AVALIACAO EQUACOES DIFERENCIAIS pdf

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Correta
(A)
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Correta
(C)
Pergunta 1 -- /0,6
Encontre a solução geral da seguinte equação diferencial separável 
fraction numerator d t over denominator d x end fraction equals fraction numerator 8 t over denominator x plus 
5 end fraction
Resposta corretat left parenthesis x right parenthesis equals k left parenthesis x plus 5 right 
parenthesis to the power of 8
t left parenthesis x right parenthesis equals k left parenthesis x plus 5 right parenthesis to the power of 
18
t left parenthesis x right parenthesis equals minus k left parenthesis x plus 5 right parenthesis to the 
power of 8
t left parenthesis x right parenthesis equals k left parenthesis x minus 5 right parenthesis to the power of 
8
t left parenthesis x right parenthesis equals k left parenthesis 5 x plus 5 right parenthesis to the power of 
8
Pergunta 2 -- /0,6
Dada a seguinte equação diferencial y apostrophe apostrophe minus 8 y apostrophe plus 16 y equals 0; qual 
o Wronskiano associado as soluções dessa equação diferencial?
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e to the power of 4 t end exponent
e to the power of 6 t end exponent
Resposta corretae to the power of 8 t end exponent
e to the power of 10 t end exponent
e to the power of t
Pergunta 3 -- /0,6
Calcule a integral usando o Teorema de Green: 
contour integral subscript c left parenthesis 2 y plus ln left parenthesis 10 x squared minus 4 right parenthesis 
d x plus left parenthesis 8 x minus square root of y to the power of 4 plus e to the power of y end root right 
parenthesis d y
 em que a curva C é o círculo x squared plus y squared equals 16
Resposta correta96 pi
36 pi
54 pi
48 pi
12 pi
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(B)
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C t
Pergunta 4 -- /0,6
Resolva o problema de valor inicial, sendo a equação diferencial dada por:
Y’’ + 2y’- y =0; y(0)=0, y’(0)= -1
Y left parenthesis t right parenthesis equals negative 1 half e to the power of 2 t end exponent plus 1 half 
e to the power of negative 2 t end exponent
Resposta correta
Y left parenthesis t right parenthesis equals negative fraction numerator square root 
of 2 over denominator 4 end fraction e to the power of t left parenthesis negative 1 plus 
square root of 2 right parenthesis end exponent plus fraction numerator square root of 2 
over denominator 4 end fraction e to the power of left parenthesis negative 1 minus 
square root of 2 right parenthesis t end exponent
Y left parenthesis t right parenthesis equals negative fraction numerator square root of 2 over 
denominator 4 end fraction e to the power of t left parenthesis 1 plus square root of 2 right parenthesis end 
exponent plus 1 half e to the power of negative 2 t end exponent
Y left parenthesis t right parenthesis equals negative fraction numerator square root of 2 over 
denominator 4 end fraction e to the power of t left parenthesis negative 1 plus square root of 2 right 
parenthesis end exponent plus 1 half e to the power of 2 t end exponent
Y left parenthesis t right parenthesis equals e to the power of t left parenthesis 1 plus square root of 2 
right parenthesis end exponent minus 1 half e to the power of negative 2 t end exponent
Pergunta 5 -- /0,6
A equação diferencial y’ +3y= e , está escrita na forma padrão de uma equação linear. Determine a solução da 
EDO de primeira ordem.
2x
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(C)
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Y equals negative e to the power of 2 x end exponent over 5 minus k e to the power of negative 3 x end 
exponent
Y equals e to the power of 2 x end exponent over 5 plus k
Resposta corretaY equals e to the power of 2 x end exponent over 5 plus k e to the power of negative 
3 x end exponent
Y equals e to the power of 2 x end exponent over 5
Y equals k e to the power of negative 3 x end exponent
Pergunta 6 -- /0,6
Resolva o problema de valor inicial, da equação diferencial dada por:
Y’’ + 4y’ + 4y =0; y(0)=1, y’(0)= 3
Y left parenthesis t right parenthesis equals negative 1 half e to the power of 2 t end exponent plus 1 half 
e to the power of negative 2 t end exponent
Y left parenthesis t right parenthesis equals negative fraction numerator square root of 2 over 
denominator 4 end fraction e to the power of t left parenthesis negative 1 plus square root of 2 right 
parenthesis end exponent plus fraction numerator square root of 2 over denominator 4 end fraction e to the 
power of left parenthesis negative 1 minus square root of 2 right parenthesis t end exponent
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Correta
(C) 3r² + r -1=0
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Resposta correta
Y left parenthesis t right parenthesis equals e to the power of negative 2 t end 
exponent plus 5 e to the power of negative 2 t end exponent
Y left parenthesis t right parenthesis equals negative fraction numerator square root of 2 over 
denominator 4 end fraction e to the power of t left parenthesis negative 1 plus square root of 2 right 
parenthesis end exponent plus 1 half e to the power of 2 t end exponent
Y left parenthesis t right parenthesis equals e to the power of t left parenthesis 1 plus square root of 2 
right parenthesis end exponent minus 1 half e to the power of negative 2 t end exponent
Pergunta 7 -- /0,6
Determine a equação auxiliar da EDO de segunda ordem: 
3 fraction numerator d squared y over denominator d x squared end fraction plus fraction numerator d y over 
denominator d x end fraction minus y equals 0
r² +3 r -1=0
r² - 1=0
Resposta correta3r² + r -1=0
r² - r -1=0
r² + r -1=0
Pergunta 8 -- /0,6
Das equações diferenciais abaixo, qual delas não é uma EDO de primeira ordem exata?
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(D)
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Correta
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left parenthesis y minus x cubed right parenthesis d x plus left parenthesis y cubed plus x right 
parenthesis d y equals 0
fraction numerator minus y over denominator x squared plus y squared end fraction d x plus fraction 
numerator x over denominator x squared plus y squared end fraction d y equals 0
cos left parenthesis y right parenthesis space d x minus x s e n left parenthesis y right parenthesis space 
d y equals 0
Resposta corretaleft parenthesis x y squared plus 2 right parenthesis d x plus 3 x squared y d y equals 
0
x cos left parenthesis y right parenthesis d y plus left parenthesis 2 x plus s e n left parenthesis y right 
parenthesis right parenthesis d x equals 0
Pergunta 9 -- /0,6
Calcule a integral usando o Teorema de Green: 
contour integral subscript C left parenthesis 3 y plus 1 n left parenthesis 10 x squared minus 4 right 
parenthesis d x plus left parenthesis 9 x minus square root of y to the power of 4 plus e to the power of y end root 
right parenthesis d y
 em que a curva C é o círculo x squared plus y squared equals 4
Resposta correta24 pi
12 pi
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48 pi
54 pi
96 pi
Pergunta 10 -- /0,6
Use a mudança de variáveis z = x + y para encontrar a soluçãogeral da equação diferencial de primeira ordem 
fraction numerator d y over denominator d x end fraction equals square root of x plus y end root minus 1
y equals open square brackets x over 2 plus C close square brackets squared minus 2 x
y equals open square brackets x over 4 plus C close square brackets squared minus x
y equals open square brackets x over 2 plus C close square brackets squared plus 8 x
Resposta corretay equals open square brackets x over 2 plus C close square brackets squared minus 
x
y equals open square brackets x over 2 plus C close square brackets squared minus x y