Consider Euler's method for the integration of the system of differential equations: x˙ = -y y˙ = x Assume that (xin, yin) are the points obtained for i = 0, 1, ..., n2 using a time-step h = 1/n starting at the initial point (x0, y0) = (1, 0). Which of the following statements is true?

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Mathematics · Higher Mathematics

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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(xin)2 + (yin)2 > 1 for all i ≥ 1

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Answer 1

The points (xin, yin) lie exactly on a circle of radius 1

Answer 2

limn → ∞ (xnn, ynn) = (cos(1), sin(1))

Answer 3

limn → ∞ (x2n, y2n) = (1, 0)

Answer 4

(xin)2 + (yin)2 > 1 for all i ≥ 1

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