Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?
1 answer:
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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Hope this helps! :)
Answer:
B. -t+8
Step-by-step explanation:
add t to -2t and add 3 and 5
2nd, 4th, and 5th answers are correct