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Consider the system x'=xy+y2 and y'=x2 -3y-4. Find all four equilibrium points and linearize the system...

Consider the system x'=xy+y2 and y'=x2 -3y-4. Find all four equilibrium points and linearize the system around each equilibrium point identifying it as a source, sink, saddle, spiral source or sink, center, or other. Find and sketch all nullclines and sketch the phase portrait. Show that the solution (x(t),y(t)) with initial conditions (x(0),y(0))=(-2.1,0) converges to an equilibrium point below the x axis and sketch the graphs of x(t) and y(t) on separate axes.

Please write the answer on white paper using black and orient it properly so that it can be easily read.

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