Let y (t), z (t) functions and L {y (t)} (s) = Y (s), L {z (t)} = Z (s) their Laplace transforms. These functions satisfy: (img3) (a) Determine the values of α and β such that Y (s) = 17 / (s + 1) ^ 3. (b) Explicitly determine the functions y (t) and z (t) that solve the problem.

Let y (t), z (t) functions and L {y (t)} (s) = Y (s), L {z (t)} = Z (s) their Laplace transforms. These functions satisfy: (img3) (a) Determine the values of α and β such that Y (s) = 17 / (s + 1) ^ 3. (b) Explicitly determine the functions y (t) and z (t) that solve the problem.

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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Question

Let y (t), z (t) functions and L {y (t)} (s) = Y (s), L {z (t)} = Z (s) their Laplace transforms. These functions satisfy:
(img3)

(a) Determine the values of α and β such that Y (s) = 17 / (s + 1) ^ 3.

(b) Explicitly determine the functions y (t) and z (t) that solve the problem.

y" (t) + y' (t) + y(t) + [i By(x)ea(t-z)dx – 17e at
y(0) = 0
y' (0) = 0
Y(s)
0 =
e17s Z(s)
17

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