Consider a system governed by the following equations: d x_1 ( t ) dt…

Question

Consider a system governed by the following equations:

\frac{d x _{1} ( t )}{dt} = x_{2} (t) - x_{1} (t); \frac{d x _{2} ( t )}{dt} = x_{1} (t) - x_{2} (t)

The initial conditions are such that

x_{1} (0) < x_{2} (0) < \infty.

Let

x_{1 f} = t \to \infty lim x_{1} (t)

and

x_{2 f} = t \to \infty lim x_{2} (t) .

Which one of the following is true?

Accepted Answer

Option C. x_1 f = x_2 f <. Answer & Solution Answer: Option C No explanation is given for this question Let's Discuss on Board

Consider a system governed by the following equations: d x_1 ( t ) dt = x_2 ( t ) - x_1 ( t );\, d x_2 ( t ) dt = x_1 ( t ) - x_2 ( t ) The initial conditions are such that x_1 ( 0 ) < x_2 ( 0 ) < . Let x_1 f = _ t x_1 ( t ) and x_2 f = _ t x_2 ( t ). Which one of the following is true?