Mathematics · Ordinary Differential Equations
Let f : &DoubleStruckCapitalR;2 → &DoubleStruckCapitalR;2 be a non-zero smooth vector field satisfying div(f) ≠ 0 everywhere. According to the Bendixson-Dulac theorem, which of the following statements is necessarily true for the autonomous system of ODEs x' = f(x)?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1All solutions are unbounded
- 2All solutions are bounded
- 3There are no periodic solutions✓
- 4There are no equilibrium points
Correct answer
There are no periodic solutions
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