1. Consider the system x' = 3x +2y y' = -x (a) Find the general solution...

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1. Consider the system x' = 3x +2y y' = -x (a) Find the general solution of the system. (b) Determine the type of the equilibrium at the origin. (c) (d) • in a saddle/node case, show the eigenvectors and the ray solutions. • in a center/spiral case, determine the direction of rotation. Determine the stability of the equilibrium at the origin. Sketch trajectories in the phase plane. Moreover, 1. Consider the system x' = 3x +2y y' = -x (a) Find the general solution of the system. (b) Determine the type of the equilibrium at the origin. (c) (d) • in a saddle/node case, show the eigenvectors and the ray solutions. • in a center/spiral case, determine the direction of rotation. Determine the stability of the equilibrium at the origin. Sketch trajectories in the phase plane. Moreover,