See answer: In each of 5 through 18:(a) Determine all critical points of the given

Chapter 9, Problem 15

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In each of 5 through 18:(a) Determine all critical points of the given system of equations.(b) Find the corresponding linear system near each critical point.(c) Find the eigenvalues of each linear system. What conclusions can you then draw aboutthe nonlinear system?(d) Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extendthem in those cases where the linear system does not provide definite information about thenonlinear system.dx/dt = 2x y x(x2 + y2), dy/dt = x y + y(x2 + y2)

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