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For each of the following problems (even the book ones) do the following: a. Use the x-...

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Advance Math

For each of the following problems (even the book ones) do thefollowing:

a. Use the x- and y- nullclines to find all the equilibriumpoints.

b. Compute the Jacobian matrix of the system.

c. Determine the type of each equilibrium point (if it is ahyperbolic equilibrium).

d. Plot the phase portrait in CoCalc.

1. dx/dt = x-xy-8x^2

dy/dt = -y+xy

2. dx/dt = x-y+x^2

dy/dt = x+y

3. dx/dt = 8x-4x^2-xy

dy/dt = 3y-3xy-y^2

4. dx/dt = y-x^2y

dy/dt = -x+xy^2

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