Question: 3. Consider a process that can be modelled with the differential equation: dx = 2cx + 4axy + 6by - 8 dt where x is

3. Consider a process that can be modelled with the differential

3. Consider a process that can be modelled with the differential equation: dx = 2cx + 4axy + 6by - 8 dt where x is the dependent variable, a, b, and c are constants, and y is an input variable. At t=0, x=xs. a) Linearize the equation and introduce deviation variables. Find the Laplace transform of the equation.|| b) c) Find an expression for the time constant. d) Find an expression for the gain. e) Find an expression for the transfer function. Find x(t) if we introduce a step change of magnitude 1 at t=0. f)

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