Laplace Transform: Solving y''-2y'+2y=0

[Tom1]

Homework Statement

y''-2y'+2y = 0

Homework Equations

y(0)=0
y'(0)=1

The Attempt at a Solution

e^at sin(bt)

I did this problem earlier with some help, but if someone could post the steps along the way so I could do a few more similar to it, I would appreciate it.

 

[Defennder]

Where's your problem? Do you have problems finding the inverse Laplace transform once you are done with substituting the initial values?

Can you get this expression:

$$L(y) \ = \frac{1}{s^2-2s+2}$$