12y"(t) + 8y'(t) + 6y(t) = 4x(t) + 2 2. (25 points) For the following differential equation: where x(t) is a forcing function and y(0) = 1/3. (a) Convert the equation to deviation variable form. (b) Showing your work in detail, state specifically whether y(t) is stable or unstable. If y(t) is stable, is it oscillatory or monotonic? 4. (25 points) Consider a constant temperature CSTR where a second order reaction occurs. The following parameters are constant: volumetric flow rate F into the reactor, reactor volume V, and temperature T. The inlet concentration is CAD(t) and the reactor outlet concentration is CA(t). A species balance yields an ODE that describes concentration of species A in the tank as a function of time. When that ODE is linearized, it has the form: IC,(1) + [# + 2kC As ] C (0) = KC + EC(0) dt A.S where C(0)=CAS Showing all steps, derive equations for the time constant and all of the gain factors for this process at concentration CAS Note: you need not derive the ODE shown above. You may assume it is correct