Exercises 5.4figure indicates that (0,0) is a stable critical point (center) whereas (1,0) is a saddle point(unstable).25.This system has two critical points, (0,0) and (1,0), which are solutions to the systemy= 0,−x+x3= 0.The direction field for this system is depicted in Figure B.37. From this figure we concludethat(a)the solution passing through the point (0.25,0.25) ﬂows around (0,0) and thus is periodic;(b)for the solution (x(t), y(t)) passing through the point (2,2),y(t)→ ∞ast→ ∞, and sothis solution is not periodic;(c)the solution passing through the critical point (1,0) is a constant (equilibrium) solutionand so is periodic.27.The direction field for given system is shown in Figure B.38 in the answers of the text. Fromthe starting point, (1
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