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,

$\displaystyle

y(t) + \int_{0}^{t} e^{2(t - T)} . y(T) . dT = e^{2t} - t

$

where T is supposed to be tau.

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

$\displaystyle

y(t) = e^{2t} - t - $(y * $\displaystyle e^{2}$)(t)

where (y * $\displaystyle e^{2}$)(t) is the convolution

i then took la place transforms to give;

$\displaystyle

L(y(t)) = \frac{1}{s-2} - \frac{1}{s^{2}} - (L(y(t)) . \frac{1}{s-2}

$

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,