I want a handwritten solution eithout using ai$.!!!$

Consider the feedback control system below. The plant is given as $G_p(s)=\frac{2+s}{s^2+2s+2}.$

a$.$ Write the differential equation $($DE$)$ of the plant.

b$.$ Let $G_c(s)=\frac{2s}{s+2}$ and $H(s)=\frac{1}{s+1}.$ Find the DE of the overall system.

c$.$ Let $T=0\mathrm{.}1s.$ Find the difference equation corresponding to $G_p(s).$ Note: Timederivative can be approximated b

y $\frac{df}{dt}{|}_t||=kT$~$=\frac{f(kT)-f(kT-T)}{T}$