If I know $Y(s)$, can I predict when $\mathscr{L}^{-1}[Y(s)]=y(t)$ will be continuous or continuously differentiable or even stronger conditions?
For example; I'm solving an ODE with the Laplace Tranform method so it turns out that the solution is $\mathscr{L}^{-1}[Y(s)]=y(t)$. How do I know that that function will be countinuously differentiable up to the order of the ODE?