Can't seem to get this DE solved using laplace transforms

[1MileCrash]

Homework Statement

y''-4y'+4y = 0
y(0)=1, y'(0)=1

Homework Equations

The Attempt at a Solution

This is annoying, because it feels very easy and I don't know why I am not getting the answer. Skipping the routine:

s^2L{y} - s - 1 - 4sL{y} + 4 + 4L{y} = 0

(s+3) / (s^2 - 4s + 4) = L{y}

= s/(s-2)^2 + 3/(s-2)^2

= 1/(s-2) + 2(1/(s-2)^2) +3(1/(s-2)^2)

= 5(1/(s-2)^2) + 1/(s-2)


The inverse transform of which gives:

5te^2t + e^2t = (5t+1)e^2t


Any ideas?

Thanks!

 

[1MileCrash]

NVM, I think it should be s-3 in num now.

 

[vela]

Check your signs.

EDIT: Ah, I see you found the mistake.