Use the PoincarBendixson theorem to show that the secondorder nonlinear differential
Chapter 11, Problem 18(choose chapter or problem)
Use the Poincaré-Bendixson theorem to show that the second-order nonlinear differential equation
\(x^{\prime \prime}=x^{\prime}\left[1-3 x^{2}-2\left(x^{\prime}\right)^{2}\right]-x\)
has at least one periodic solution. [Hint: Find an invariant annular region for the corresponding plane autonomous system.]
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