Question

y"+2y'+y=0, y(0)=2, y(1)=2
use the Laplace transform

Answer 1

Apply the idea...

\([s^{2}Y(s) - s\cdot y(0) - y'(0)] + 2[sY(s)-y(0)] + Y(s) = YouTellMe\)

What is the Laplace Transform of 0? This gives the right hand side.
Substitute the given values for y(0) and y'(0)
Solve for Y(s) and you'll nearly be done.