Mathematics · Ordinary Differential Equations

Let x and y be continuously differentiable functions on [0, ∞) that satisfy the respective initial value problems: dx dt + (sin t - 1)x = log(1 + t), x(0) = 1; dy dt + (sin t - 1)y = t, y(0) = 2. Define z(t) = y(t) - x(t) for t ≥ 0. Which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

z(1) > 1

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Let x and y be continuously differentiable functions on [0, &infin;) that satisfy the respective initial value problems: dx dt + (sin t - 1)x = log(1 + t), x(0) = 1; dy dt + (sin t - 1)y = t, y(0) = 2. Define z(t) = y(t) - x(t) for t &ge; 0. Which of the following statements is true?