Chapter 9.7, Problem 11P

To determine

(a)

The differential equations that govern the behavior of $A_1$ and

To determine

(b)

To define:

The constant $\beta$ and to show that the eigenvalues in (a) are ${\lambda }_1=0$ and ${\lambda }_2=-\frac{1+\beta }{\beta V_1}{r}_{21}$

To determine

(c)

The value of $A_1$ and $A_2$ having $A_1(0)={\alpha }_1$ and $A_2(0)={\alpha }_2$,

To determine

(c)

To show:

The given result $\underset{t\to +\infty }{\lim }\frac{A_1}{V_1}=\underset{t\to +\infty }{\lim }\frac{A_2}{V_2}=\frac{{\alpha }_1+{\alpha }_2}{(1+\beta )V_1}$