Consider the second-order ordinary differential equation (ODE) x'' + p(t)x' + q(t)x = 0, where p(t) and q(t) are continuous functions on [a, b]. Let x1 and x2 be two solutions of this ODE. Which of the following statements is true for the Wronskian W of x1 and x2?

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Mathematics · Differential Equations

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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W(t0) = 0 for some t0 ∈ (a, b) implies that W ≡ 0 in (a, b)

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Answer 1

W(t0) = 1 for some t0 ∈ (a, b) implies that W ≡ 1 in (a, b)

Answer 2

W(t0) = 0 for some t0 ∈ (a, b) implies that W ≡ 0 in (a, b)

Answer 3

W can change its sign inside the interval (a, b)

Answer 4

W ≡ 0 in (a, b) implies that x1, x2 are linearly independent

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