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Problem 1. Determine the stability of the critical point of the system: (a) X-=r+y-2x2 = - (1) Y'=-2x+y+3yz = (b) - (2) y' = - 2.c - 4y + ysin(x) Problem 2. Consider the system x' = =4r+4y-r(r²+y²) - (3) y' = - -4.c + 4y - y(x² + y2) (a) Show that there a closed path in the region 1r: 3, where r2 = x2 + y2. (b) Find the general solution. Problem 3. Study the stability properties of the critical point (0,0) for H = 0, > 0, < 0 for the system = - - (4) = - Problem 4. Show that x" + x' + f(x) = 0 has no periodic solution. Problem 5. Determine the region on which there is no periodic solution for x"+B(x2. - 1)x' + x = 0 (5)

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