3. For the system dx dt ux ty - yx2 dy dt = -x + uy + 33' (a) (4 points) Classify the critical point at (0, 0) in terms of / by finding the eigenvalues. (b) (8 points) There is a Hopf bifurcation at / = 0. Determine if it is supercritical or subcrit- ical.(c) (6 points) Sketch the solutions to the system for u 0. (d) (6 points) Suppose (r(t), y(t)) is a solution to the system, where r(0) and y(0) are both small. Sketch the function x(t) for A 0