GATE EE 2018 Set 1 — Question 43

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MCQ+2 / -0.67MediumFirst-Order EquationsDifferential EquationsEngineering MathematicsSolution of State EquationsState-Space AnalysisControl Systems

Control Systems → Differential Equations → First-Order Equations

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Question

Consider a system governed by the following equationsdx1(t)dt=x2(t)x1(t)\frac{dx_1(t)}{dt} = x_2(t) - x_1(t)dx2(t)dt=x1(t)x2(t)\frac{dx_2(t)}{dt} = x_1(t) - x_2(t)The initial conditions are such that x1(0)<x2(0)<x_1(0) < x_2(0) < \infty. Let x1f=limtx1(t)x_{1f} = \lim_{t \to \infty} x_1(t) and x2f=limtx2(t)x_{2f} = \lim_{t \to \infty} x_2(t). Which one of the following is true?
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