Question

Find the Laplace transform of the function y(t) if y(t) satisfies the differential equation d^2y/dt^2 - 4dy/dt + 3y = 9e^-4t, y(0) = 0, y'(0) = 3 Your answer should be expressed as a function of s using the correct syntax. Laplace transform is Y(s) =

          Find the Laplace transform of the function y(t) if y(t) satisfies the differential equation
d^2y/dt^2 - 4dy/dt + 3y = 9e^-4t, y(0) = 0, y'(0) = 3
Your answer should be expressed as a function of s using the correct syntax.
Laplace transform is Y(s) =

Find the Laplace transform of the function y(t) if y(t) satisfies the differential equation
d^2y/dt^2 - 4dy/dt + 3y = 9e^-4t, y(0) = 0, y'(0) = 3
Your answer should be expressed as a function of s using the correct syntax.
Laplace transform is Y(s) =

Added by Miguel B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/07/2023

Step 1

The Laplace transform of the second derivative is given by: $$\mathcal{L}\{y''(t)\} = s^2Y(s) - sy(0) - y'(0)$$ Since $y(0) = 0$ and $y'(0) = 3$, we have: $$\mathcal{L}\{y''(t)\} = s^2Y(s) - 3$$ The Laplace transform of the first derivative is given Show more…

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Find the Laplace transform of the function y(t) if y(t) satisfies the differential equation d^2y/dt^2 - 4dy/dt + 3y = 9e^-4t, y(0) = 0, y'(0) = 3. Your answer should be expressed as a function of s using the correct syntax: Laplace transform is Y(s) =