How can I use Mathematica to resolve a Initial value problem involving Laplace-Transform?
For example:
Solve, using Laplace Transform, the following Initial value problem in [0,+∞]$$ \begin{cases} y'' - y = f(t) \\ y (0) = 0 \\ y' (0)=0 \end{cases}$$
$$f(t)= \begin{cases} t^2 && -1<t<0 \\ 1 && t>1 \end{cases}$$
