I am quite stuck with the following differential equation: $$y'(t)+y(t-1)=t^2 \quad \text{with} \: y(t)=0 \; \text{for} \; t\leq 0.$$ I would like to use Laplace transform to solve this one. Using different properties I manage to find the following relation: $$p \, Y(p)+e^{-p} \, Y(p)=\frac{2}{p^3}$$ Isolating $Y(p)$, $$Y(p)=\frac{2}{p^3(p+e^{-p})}=\frac{2}{p^4}\cdot\frac{1}{1+\frac{e^{-p}}{p}}$$ But now I am stuck, I think I would like to express the solution as a series but I can't find the series expansion of the right member.
Anyone has a clue?
Thanks in advance.