Question

Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y'' - 2y' - 24y = { 1, 0 <= t < 1; 0, 1 <= t, y(0) = 0, y'(0) = 0 Y(s) = Now find the inverse transform: y(t) = (Notation: write u(t-c) for the Heaviside step function uc(t) with step at t = c.) Note: 1 / (s(s - 6)(s + 4)) = (-1/24)/s + (1/40)/(s + 4) + (1/60)/(s - 6)

          Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}:
y'' - 2y' - 24y = { 1, 0 <= t < 1; 0, 1 <= t, y(0) = 0, y'(0) = 0
Y(s) =
Now find the inverse transform:
y(t) =
(Notation: write u(t-c) for the Heaviside step function uc(t) with step at t = c.)
Note:
1 / (s(s - 6)(s + 4)) = (-1/24)/s + (1/40)/(s + 4) + (1/60)/(s - 6)

Take the Laplace transform of the following initial value problem and solve for Y(s) = Ly(t):
y” - 2y' - 24y = 1, 0 <= t < 1; 0, 1 <= t, y(0) = 0, y'(0) = 0
Y(s) =
Now find the inverse transform:
y(t) =
(Notation: write u(t-c) for the Heaviside step function uc(t) with step at t = c.)
Note:
1 / (s(s - 6)(s + 4)) = (-1/24)/s + (1/40)/(s + 4) + (1/60)/(s - 6)

Added by Douglas P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/07/2023

Step 1

First, we take the Laplace transform of the differential equation and the initial conditions: s^2 Y(s) - s y(0) - y'(0) - 2Y(s) - AY(s) = 8/s - 8/s e^(-s) Since y(0) = 0 and y'(0) = 0, we can simplify this to: s^2 Y(s) - 2Y(s) - AY(s) = 8/s - 8/s e^(-s) 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' - 24y = { 1, 0 <= t < 1; 0, 1 <= t y(0) = 0, y'(0) = 0 Y(s) = Now find the inverse transform: y(t) = (Notation: write u(t-c) for the Heaviside step function uc(t) with step at t = c.) Note: