Question

Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y'' - 2y' - 35y = {1, 0 ? t < 1; 0, 1 ? t, y(0) = 0, y'(0) = 0 Y(s) = Now find the inverse transform to find y(t) = (Use step(t-c) for uc(t) .) Note: 1 / (s(s - 7)(s + 5)) = (-1/35)/s + (1/60)/(s + 5) + (1/84)/(s - 7)

          Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}:
y'' - 2y' - 35y = {1, 0 ? t < 1; 0, 1 ? t, y(0) = 0, y'(0) = 0
Y(s) =
Now find the inverse transform to find y(t) =
(Use step(t-c) for uc(t) .) Note:
1 / (s(s - 7)(s + 5)) = (-1/35)/s + (1/60)/(s + 5) + (1/84)/(s - 7)

Take the Laplace transform of the following initial value problem and solve for Y(s) = Ly(t):
y” - 2y' - 35y = 1, 0 ? t < 1; 0, 1 ? t, y(0) = 0, y'(0) = 0
Y(s) =
Now find the inverse transform to find y(t) =
(Use step(t-c) for uc(t) .) Note:
1 / (s(s - 7)(s + 5)) = (-1/35)/s + (1/60)/(s + 5) + (1/84)/(s - 7)

Added by Randy N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/16/2023

Step 1

To do this, we need to factor the denominator of Y(s) and use partial fraction decomposition: Y(s) = A / (s+5) + B / (s-7) + (Cs + D) / (s^2 - 35s - 10) Multiplying both sides by the denominator of Y(s), we get: 35 = A(s-7)(s^2 - 35s - 10) + B(s+5)(s^2 - 35s - Show more…

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Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y'' - 2y' - 35y = {1, 0 ≤ t < 1; 0, 1 ≤ t y(0) = 0, y'(0) = 0 Y(s) = Now find the inverse transform to find y(t) = (Use step(t-c) for uc(t) .) Note: 1 / (s(s - 7)(s + 5)) = (-1/35)/s + (1/60)/(s + 5) + (1/84)/(s - 7)