Laplace DE with unit step function

Just a quick question on a laplace transform question,

I need to find the transform for

y" +2y' + y = u(t-1) , y(0)=1, y'(0)= -1

After using the known properties i obtained,

Y(s) = exp(-s)[1/(s(s-1)^2)] + (s^2+s)/(s(s-1)^2)

using partial fractions, t-shifting and s-shifting and other known properties i arrived at

y(t) = (1+exp(t-1)((t-1)-1))u(t-1) + exp(t)(1+t)

Thus for 0<t<1

y(t) =exp(t)(1+t)

for t>1

y(t)= 1+exp(t-1)((t-1)-1) + exp(t)(1+t)

Is my answer and methodology correct? There is no answer in the book.

Thanks for your help.

Re: Laplace DE with unit step function

I think you might have some sign errors in there somewhere. Taking the LT of the original DE yields

which leads to

I end up with the LT being

You can use partial fractions on the first to obtain

Can you finish from here?