Mathematics · Ordinary Differential Equations
For b ∈ ℝ, let yb = yb(x) be the unique solution of the initial value problem: dydx = y5 + y4 + y3 + y2 + y + 1, y(0) = b defined on its maximal interval of existence Ib. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There exists an a ∈ (-∞, 0) such that for every b ∈ ℝ with b < a, the solution yb is bounded below on Ib.
- 2There exists an a ∈ (-∞, 0) such that for every b ∈ ℝ with b < a, the solution yb is bounded above on Ib.
- 3There exists an a ∈ (0, ∞) such that for every b ∈ ℝ with b > a, the solution yb is bounded below on Ib.✓
- 4There exists an a ∈ (0, ∞) such that for every b ∈ ℝ with b > a, the solution yb is bounded above on Ib.
Correct answer
There exists an a ∈ (0, ∞) such that for every b ∈ ℝ with b > a, the solution yb is bounded below on Ib.
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