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4. Cons the system [ begin{array}{I} frac{dx}{d t}=y(x+y-1) frac{d y}{d t}=x(y-x). end{array} ] (a) Find the and X Y -nullclines of the system.
4. Cons the system \[ \begin{array}{I} \frac{dx}{d t}=y(x+y-1) \\ \frac{d y}{d t}=x(y-x). \end{array} \] (a) Find the and X Y -nullclines of the system. Sketch and label the nullclines on the graph below. Be sure to indicate the direction of the solution on the nullelines. (b) Find all of the equilibrium solutions for the system. Label these on the graph below. (c) Sketch the trajectory of a solution curve starting at and x(0) = 1 y(0) = 1 on the graph below.
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