Chapter 8.3, Problem 11E

(a)

To determine

To construct: A mathematical model in the form of a linear system of first order differential equations and to write the system in matrix form.

(b)

To determine

To solve: The linear system in (a) using the method of undetermined coefficients with subject to conditions $x_1\left(0\right)=60$ and $x_2\left(0\right)=10$.

(c)

To determine

The values of $\underset{t\to \infty }{\lim }{x}_1\left(t\right),\underset{t\to \infty }{\lim }{x}_2\left(t\right)$ and interpret the result.

(d)

To determine

To sketch: The graphs of $x_1\left(t\right)\text{ and }{x}_2\left(t\right)$ on the same coordinate axes using a graphing utility.