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cricket20 [7]
3 years ago
12

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 7y = sin(x)

.
Mathematics
1 answer:
Elza [17]3 years ago
4 0
The first thing we must do in this case is find the derivatives:
 y = a sin (x) + b cos (x)
 y '= a cos (x) - b sin (x)
 y '' = -a sin (x) - b cos (x)
 Substituting the values:
 (-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
 We rewrite:
 (-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
 sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
 sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
 From here we get the system:
 -b-8a = 1
 a-8b = 0
 Whose solution is:
 a = -8 / 65
 b = -1 / 65
 Answer:
 
constants a and b are:
 
a = -8 / 65
 
b = -1 / 65
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Answer:

Step-by-step explanation:

A = [(3x2)/2] + [(4x2)/2] - 1/2

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3 years ago
When 2/3 of a number is increased by 20, the sum is then halved, the result obtained is the same as 2/3 of the number, increased
aleksklad [387]

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4 0
3 years ago
Evaluate the expression w 2 - v + 1 for w = -2 and v = -8.
Aleksandr [31]

Answer:

Is the w2, w(2) or

{w}^{2}

?

If it's w(2) the answer is -4--8+1=-4+8+1=5

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2 years ago
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lina2011 [118]

Answer:2In2-2In3

Step-by-step explanation:

In(4/9)

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Question 2 is 19.4 I hope I helped!
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3 years ago
Read 2 more answers
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