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4. (14 pts.) Consider the One parameter family of linear systems 1 2 ,_ a u 18) Y(l 0 Y. (a) (5 pts.) Find all

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4. (14 pts.) Consider the One parameter family of linear systems 1 2 ,_ a u 18) Y(l 0 Y. (a) (5 pts.) Find all bifurcation values of a and describe the different types of phase portraits that are exhibited by this family as a varies. (b) (9 pts.) Sketch a phase portrait and write down the general solution for the system for a = 3, 2, 4. Make sure you plot enough trajectories to make it clear What the trajectory through any arbitrary point might look like

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