I am suppose to solve the following equation using laplace transforms and have started but am both unsure if i'm going about it the right way and where to go next,

where T is supposed to be tau.

i re-arranged the equation to have y(t) = the rest , then used convolution theorem to say;

(y * )(t)

where (y * )(t) is the convolution

i then took la place transforms to give;

From here i simplify but end up with terms i can't take the inverse laplace transform of in order to solve, so am thinking i must ahve gone wrong up to this point?

Can anyone help here?

Cheers,