example 5.12    p.76

gs = 1/(s^2 + 2 s + 1)
y0s = 1 (-s + 1) + 2 (-1)
y1s = gs y0s
y2s = gs  LaplaceTransform[Exp[-t], t, s]

ys = Apart[Simplify[y1s + y2s]]

yt = InverseLaplaceTransform[ys, s, t]

Plot[yt, {t, 0, 10}, PlotRange ->  {-1, 0.2}]