I have been working on this hw set all weekend and it just isn't clicking!! Any help would be greatly appreciated.

Solve the given initial value problems by Laplace transforms. Show the details of your work.

1.

y" + 9y = {

6 sin t if 0 <= t <= pi

0 if t > pi, y(0) = 0, y'(0) = 0

}

2.

y" - 2y' + 2y = 8e^(-t)cos t ; y(0) = 16; y'(0) = -16