(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).
