Question

Use the Laplace transform to solve the following initial value problem:

y′′ + 8y ′+ 16y = 0

y(0) = −3 , y′(0) = −3

First, using Y for the Laplace transform of y(t)y, 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+a)^2)
Y(s) = _________________ + ________________________

Now by inverting the transform, find y(t) = ______________________

Answer 1