(Solved): A) A system obeys the differential equation \[ 3 \ddot{y}+12 \dot{y}+9 y=9 \dot{u}+14 u(t) \] Find ...

A) A system obeys the differential equation \[ 3 \ddot{y}+12 \dot{y}+9 y=9 \dot{u}+14 u(t) \] Find the complete response when the initial conditions are \( y(0)=2, \dot{y}(0)=0 \) and when the input is \( u(t)=3 \epsilon^{-2 t} \) for \( t>0 \) and zero otherwise. B) Repeat Problem (A) when \( y(0)=2 \) and \( \dot{y}(0)=0 \) and when \( u(t)=6 \cos 2 t \) for \( t>0 \) and zero otherwise.