solution of differential equations through laplace transform and matrix method pdf code example

Example: laplace transform for differential equations mathmatica

lap = LaplaceTransform[ y''[t] - y[t] == f[t], t, s ] /. {y[0] -> 0, y'[0] -> 0};
sol = Solve[ lap, LaplaceTransform[y[t], t, s]];
InverseLaplaceTransform[ sol[[1, 1, 2]], s, t]