I'm trying to solve this problem
$\begin{cases} X'(t) + Y(t) = 2e^{2t}+e^{t}+1 \\ X(t)-Y'(t)=e^{2t}-e^{t}+1 \end{cases}$
The first thing I've done is the Laplace transform ($x(p)$ for $L[X(t)]$ and $y(p)$ for $L[Y(t)]$)
$\begin{cases} px(p)+y(p) = \frac{2}{p-2}+\frac{1}{p-1}+\frac{1}{p}\\ x(p)-py(p)=\frac{1}{p-2}-\frac{1}{p-1}+\frac{1}{p}\end{cases}$
But when I saw the solutions my professor gave us, they had used $-\frac{1}{p}$ as the Laplace transform of 1, why is that so?
Thank you