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This worksheet covers finding equilibrium points and classifying them using the jacobian matrix for a given system of differential equations. It also requires sketching phase portraits and nullclines, and analyzing the behavior of solutions with given initial conditions.
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MATH225 – Worksheet #10 Name:__________________________ Sec:________ You must show all of your work to get full credit.
dx dy dt = x (^2) " 2 xy + 2 x a. Find all equilibrium points^ dt^ =^ y^2 +^ xy^ +^8 y b. Using the Jacobian matrix, classify all equilibrium points.
c. For each equilibrium point sketch the phase portrait of the system near that point. Sketch each of these graphs separately.
dx dy dt = x (^2) " 2 xy + 2 x a. indicate the direction of the vector field along each nullcline. On the entire xy-plane, sketch the x and y nullclines and^ dt^ =^ y^2 +^ xy^ +^8 y
b. From the nullclines find all the equilibrium points
