Question: In each of Problems 12 through 16, a second-order equation of the form x'' + f (x, x') = 0, corresponding to a certain mass-and-spring

In each of Problems 12 through 16, a second-order equation of the form x'' + f (x, x') = 0, corresponding to a certain mass-and-spring system, is given. Find and classify the critical points of the equivalent first-order system.

x'' + 4x - x2 = 0: Here the force function is nonsymmetric. Verify that the critical points resemble those shown in Fig. 9.4.13.

X FIGURE 9.4.13. The phase portrait for Problem 15.

X FIGURE 9.4.13. The phase portrait for Problem 15.

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