The nonlinear second-order differential equation m:X' + kx + kix3 = 0, fork > 0
Chapter 11, Problem 38(choose chapter or problem)
The nonlinear second-order differential equation m:X' + kx + kix3 = 0, fork > 0, represents a general model for the free, undamped oscillations of a mass m attached to a spring. If k1 > 0, the spring is called hard (see Example 1 in Section 3.11). Determine the nature of the solutions to x' + x + x3 = 0 in a neighborhood of (0, 0).
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