I have a DE
$$y' + 2y = u' - u$$ and it's transfer function was given as
$$G(s) = \dfrac{(s-1)}{(s+2)}$$
Can someone elaborate on the steps in between the conversion?
(There were no initial condition $y(0)$ and $u(0)$, hence I can't seem to figure how it was transformed)
With the assumption $y(0)=u(0)$, taking the Laplace transform of both sides$$sY(s)-y(0)+2Y(s)=sU(s)-u(0)-U(s)\\\rightarrow G(s)=\frac{Y(s)}{U(s)}=\frac{s-1}{s+2}$$