Question

Solve the third-order initial value problem below using the method of Laplace transforms.\ y''' + y'' - 32y' - 60y = -180, y(0) = 12, y'(0) = 36, y''(0) = 186\ Click here to view the table of Laplace transforms.\ Click here to view the table of properties of Laplace transforms.\ y(t) = \ (Type an exact answer in terms of $e$)

Name: Solve the third-order initial value problem below using the method of Laplace transforms.y”' + y” - 32y' - 60y = -180, y(0) = 12, y'(0) = 36, y”(0) = 186Click here to view the table of Laplace transforms.Click here to view the table of properties of Laplace transforms.y(t) = (Type an exact answer in terms of e)
Uploaded: 2023-06-21T05:12:29-08:00
Duration: 5 min 33 s
Channel: Madhur L
Description: Solve the third-order initial value problem below using the method of Laplace transforms.y”' + y” - 32y' - 60y = -180, y(0) = 12, y'(0) = 36, y”(0) = 186Click here to view the table of Laplace transforms.Click here to view the table of properties of Laplace transforms.y(t) = (Type an exact answer in terms of e)

          Solve the third-order initial value problem below using the method of Laplace transforms.\
y''' + y'' - 32y' - 60y = -180, y(0) = 12, y'(0) = 36, y''(0) = 186\
Click here to view the table of Laplace transforms.\
Click here to view the table of properties of Laplace transforms.\
y(t) = \
(Type an exact answer in terms of $e$)

Solve the third-order initial value problem below using the method of Laplace transforms.y”' + y” - 32y' - 60y = -180, y(0) = 12, y'(0) = 36, y”(0) = 186Click here to view the table of Laplace transforms.Click here to view the table of properties of Laplace transforms.y(t) = (Type an exact answer in terms of e)

Added by William C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/21/2023

Step 1

The Laplace transform of y'' is s^2Y(s) - sy(0) - y'(0) The Laplace transform of y' is sY(s) - y(0) The Laplace transform of y is Y(s) So the Laplace transform of the given differential equation becomes: s^2Y(s) - sy(0) - y'(0) + sY(s) - y(0) - 32Y(s) - 60Y(s) = Show more…

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Solve the third-order initial value problem below using the method of Laplace transforms y'' + y' - 32y - 60y = -180, v0 = 12, v0 = 36, y0 = 186 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms y(t) = 1 (Type an exact answer in terms of e)