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  3. (a) find the equilibrium solution, or critical poi

(a) Find the equilibrium solution, or critical point, of the given system. (b) Use a computer to...

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Advance Math

(a) Find the equilibrium solution, or critical point, of thegiven system.

(b) Use a computer to draw a direction field and phase portraitcentered at the critical point.

(c) Describe how solutions of the system behave in the vicinityof the critical point.

x? =?0.25x?0.75y+8, y? =0.5x+y?11.5

(d) Let x= xc+u and y= yc+v, wherexc and yc give the critical point you foundin (a). Plug these into the system and show that you obtain ahomogeneous system u? = Au for u = (u v)T .

(e) Solve the resulting homogeneous system for u and v, and showthat the solutions you obtain match the phase portrait that yougenerated in (b).

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