Mathematics · Differential Equations
Suppose x(t) is the solution of the initial value problem in ℝ2 given by ẋ = Ax, x(0) = x0, where A = 5 41 2. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1e-10t|x(t)| → 0 as t → ∞, for all x0 ≠ 0.✓
- 2e-t|x(t)| → ∞ as t → ∞, for all x0 ≠ 0.
- 3e-6t|x(t)| → 0 as t → ∞, for all x0 ≠ 0.
- 4x(t) is a bounded solution for some x0 ≠ 0.
Correct answer
e-10t|x(t)| → 0 as t → ∞, for all x0 ≠ 0.
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