Solve the initial value problem using Laplace Transforms.
Apply the Laplace transform to both sides of the equation to get
Apply the initial conditions and simplify to get
Take the Inverse Laplace Transform of both sides. I leave it for you to continue from here.
Spoiler:
For the first and third term on the RHS, use a translation theorem to make life easier. The second term on the RHS can be rewritten as . Apply translation theorems when needed.
Last edited by Chris L T521; August 30th 2009 at 11:30 PM.
Reason: fixed typo
Apply the Laplace transform to both sides of the equation to get
Apply the initial conditions and simplify to get
Take the Inverse Laplace Transform of both sides. I leave it for you to continue from here.
Spoiler:
For the first and third term on the RHS, use a translation theorem to make life easier. The second term on the RHS can be rewritten as . Apply translation theorems when needed.
is the ie. the third term of the equation supposed to be ?