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Ordinary Differential Equation

Quick practice

Question 1 of 5

Consider a system governed by the following equations $\frac{d x_{1}(t)}{d t}=x_{2}(t)-x_{1}(t)$ $\frac{d x_{2}(t)}{d t}=x_{1}(t)-x_{2}(t)$ . The initial conditions are such that $x_{1}(0)<x_{2}(0)<\infty$ .

Let $x_{1 f}=\lim _{t \rightarrow \infty} x_{1}(t)$ and $x_{2 f}=\lim _{t \rightarrow \infty} x_{2}(t)$ which one of the following is true?

A

$x_{2 f}<x_{1 f}<\infty$

B

$x_{1, f}<x_{2, f}<\infty$

C

$x_{1, f}=x_{2, f}<\infty$

D

$x_{1, f}=x_{2, f}=\infty$

Concepts

Solution of Linear Differential Equations with Constant and Variable Coefficients

Linear Equations of Second Order