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a. Consider the initial value problem: y" – 4y' + 8 y = 0 y (0) = 0, y' (0) = 2 Which of the following is the Laplace transform of the DE? (Note that L{f(t)}=L[f(t)). O L{y} (s² – 4 s + 8) + (8 – s)y (0) – y' (0) O L{y} (s² – 4 s + 8) + (8 + s)y (0) – y' (0) o L{y} (s² – 4 s + 8) + (4 – s)y (0) – y' (0) O L{y} (s² – 4 s + 8) + (8 – s)y (0) +y' (0) b. Which of the following is the function Y (s) that needs to be inverted in order to solve the DE? O Y (s) = 2 (s–1)²–2² O Y (s) = 2 (s–2)2+1² O Y (s) (s–1)²+2² O Y (s) (s–2)²+2? c. Using the function Y (s) determined in the previous step, write down the solution of the initial value problem. use "exp(ab)" for the exponential functions. (Note: decimal approximations are not acceptable.) y (t) =

a. Consider the initial value problem: y" – 4y' + 8 y = 0 y (0) = 0, y' (0) = 2 Which of the following is the Laplace transform of the DE? (Note that L{f(t)}=L[f(t)). O L{y} (s² – 4 s + 8) + (8 – s)y (0) – y' (0) O L{y} (s² – 4 s + 8) + (8 + s)y (0) – y' (0) o L{y} (s² – 4 s + 8) + (4 – s)y (0) – y' (0) O L{y} (s² – 4 s + 8) + (8 – s)y (0) +y' (0) b. Which of the following is the function Y (s) that needs to be inverted in order to solve the DE? O Y (s) = 2 (s–1)²–2² O Y (s) = 2 (s–2)2+1² O Y (s) (s–1)²+2² O Y (s) (s–2)²+2? c. Using the function Y (s) determined in the previous step, write down the solution of the initial value problem. use "exp(ab)" for the exponential functions. (Note: decimal approximations are not acceptable.) y (t) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a. Consider the initial value problem: y" – 4y' + 8 y = 0 y (0) = 0, y' (0) = 2 Which of the following is the Laplace transform of the DE? (Note that L{f(t)} =L[f(t)). L{y} (s² – 4 s + 8) + (8 – s)y (0) – y' (0) O L{y} (s² – 4 s+8) + (8 + s)y (0) – y' (0) o L{y} (s² – 4 s + 8) + (4 – s)y (0) – y' (0) O L{y} (s² – 4 s +8) + (8 – s)y (0) + y' (0) b. Which of the following is the function Y (s) that needs to be inverted in order to solve the DE? O Y (s) = 2 (s-1)2–22 O Y (s) (s-2)+12 O Y (s) 2 (8-1)+22 Y (s) = (s–2)²+2² c. Using the function Y (s) determined in the previous step, write down the solution of the initial value problem. use "exp(ab)" for the exponential functions. (Note: decimal approximations are not acceptable.) y (t) =
Transcribed Image Text:a. Consider the initial value problem: y" – 4y' + 8 y = 0 y (0) = 0, y' (0) = 2 Which of the following is the Laplace transform of the DE? (Note that L{f(t)} =L[f(t)). L{y} (s² – 4 s + 8) + (8 – s)y (0) – y' (0) O L{y} (s² – 4 s+8) + (8 + s)y (0) – y' (0) o L{y} (s² – 4 s + 8) + (4 – s)y (0) – y' (0) O L{y} (s² – 4 s +8) + (8 – s)y (0) + y' (0) b. Which of the following is the function Y (s) that needs to be inverted in order to solve the DE? O Y (s) = 2 (s-1)2–22 O Y (s) (s-2)+12 O Y (s) 2 (8-1)+22 Y (s) = (s–2)²+2² c. Using the function Y (s) determined in the previous step, write down the solution of the initial value problem. use "exp(ab)" for the exponential functions. (Note: decimal approximations are not acceptable.) y (t) =
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