Question

Transform the differential equation 6y''' + 49y'' - 54y' - 441y = 7e^-7t y(0) = 0 y'(0) = 0 y''(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). Therefore Y = = 1/(s-3) + 1/(s+3) + 1/(s+7) Taking the inverse Laplace transform we get y =

          Transform the differential equation
6y''' + 49y'' - 54y' - 441y = 7e^-7t
y(0) = 0
y'(0) = 0
y''(0) = 1
into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)).
Therefore
Y =
=
1/(s-3) + 1/(s+3) + 1/(s+7)
Taking the inverse Laplace transform we get
y =

Transform the differential equation
6y”' + 49y” - 54y' - 441y = 7e^-7t
y(0) = 0
y'(0) = 0
y”(0) = 1
into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)).
Therefore
Y =
=
1/(s-3) + 1/(s+3) + 1/(s+7)
Taking the inverse Laplace transform we get
y =

Added by Juan W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Penny Riley

Step 1

First, we take the Laplace transform of both sides of the differential equation: L{6y'' + 49y' + 54y + 44ly} = L{Te^-7t} Using the linearity property of the Laplace transform, we can split this into four separate transforms: 6L{y''} + 49L{y'} + 54L{y} + Show more…

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Transform the differential equation 6y''' + 49y'' - 54y' - 441y = 7e^-7t y(0) = 0 y'(0) = 0 y''(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y (not Y(s)). Therefore, Taking the inverse Laplace transform, we get