Question

Use the Laplace transform to solve the following initial value problem: y'' + 4y' - 21y = 0 y(0) = 2, y'(0) = -3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(s) = A/(s+a) + B/(s+b) where a < b Y(s) = + Now by inverting the transform, find y(t) = .

          Use the Laplace transform to solve the following initial value problem:
y'' + 4y' - 21y = 0        y(0) = 2, y'(0) = -3
First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation
= 0
Now solve for Y(s) =
and write the above answer in its partial fraction decomposition, Y(s) = A/(s+a) + B/(s+b) where a < b
Y(s) = + 
Now by inverting the transform, find y(t) = .

$Use the Laplace transform to solve the following initial value problem: y” + 4y' - 21y = 0 y(0) = 2, y'(0) = -3 First, using Y for the Laplace transform of y(t), i.e., Y = Ly(t), find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(s) = A/(s+a) + B/(s+b) where a < b Y(s) = + Now by inverting the transform, find y(t) = .$

Added by Michelle P.

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