Use the Poincare-Bendixson theorem to show that the secondorder nonlinear differential

Chapter 11, Problem 18

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Use the Poincare-Bendixson theorem to show that the secondorder nonlinear differential equation x' = x'[l -3i2 - 2(x')2] - x has at least one periodic solution. [Hint: Find an invariantannular region for the corresponding plane autonomoussystem.]

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