Mathematics · Differential Equations

Let x 1 (t) and x 2 (t) be the solution of the initial value problem: e -t dx 1 dt = -x 1 + x 2 e -t dx 2 dt = -x 1 - x 2 with x 1 (0) = 1, x 2 (0) = 0. If r(t) = √(x 1 2 (t) + x 2 2 (t)), then which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

r(t) → 0 as t → +∞

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Let x 1 (t) and x 2 (t) be the solution of the initial value problem: e -t dx 1 dt = -x 1 + x 2 e -t dx 2 dt = -x 1 - x 2 with x 1 (0) = 1, x 2 (0) = 0. If r(t) = &radic;(x 1 2 (t) + x 2 2 (t)), then which of the following statements is true?