Functions x(t) and y(t) are given by a system of differential equations: dx dt dy dt...

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Functions x(t) and y(t) are given by a system of differential equations: dx dt dy dt = x-3xy + 8x; a) Linearize the system for the neighborhoods of the equilibrium points. Determine the types of the equilibrium points for the linearized systems and whether they are stable or not. Do the same for the non-linear system. = x + y - 4. Functions x(t) and y(t) are given by a system of differential equations: dx dt dy dt = x-3xy + 8x; a) Linearize the system for the neighborhoods of the equilibrium points. Determine the types of the equilibrium points for the linearized systems and whether they are stable or not. Do the same for the non-linear system. = x + y - 4.

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