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3.1 The differential equation (dynamic) model for a chemical process is as follows: dt2d2y+5dtdy+3y=2u(t) where u(t) is the single input function of time. y(0) and dy/dt(0) are both zero. What are the functions of the time (e.g., e1/7) in the solution to the ODE for output y(t) for each of the following cases? (a) u(t)=be2t (b) u(t)=ct b and c are constants. Note: You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t)