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djverab [1.8K]
3 years ago
11

Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?

Mathematics
1 answer:
TiliK225 [7]3 years ago
4 0
Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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Answer:

Step-by-step explanation:

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Then combine like terms:  -2 = x, or

x = -2.

To complete the formal check, substitute -2 for x in the first equation.  This results in:

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8 0
3 years ago
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3 0
2 years ago
A lifeguard is in a look out chair and sees a person in distress. The eye level of the lifeguard is 15 feet above the ground. Th
faltersainse [42]

Answer:

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Step-by-step explanation:

Given: A lifeguard sees a person in distress.The eye level of the lifeguard is 15 feet above the ground. Angle of depression is 34°.

To find: Horizontal distance between lifeguard and the person.

Solution : If we draw a triangle then tan∅ = \frac{height}{base}

               Here base is the horizontal distance.

               Now we put the values in the formula.

               tan 34° = \frac{15}{base}

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So the answer is 22 feet.

7 0
3 years ago
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Vikentia [17]
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x=1
y=-3 so choice A.(1,-3) is right sure 

hope this will help you 

8 0
3 years ago
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Alenkinab [10]
The answer to this question is C I just worked it out on paper using a calculator

5 0
3 years ago
Read 2 more answers
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