Chapter 3.P2, Problem 2P

To determine

To prove: The system $\frac{d{x}_1}{dt}=-(K+k_{21})x_1+k_{12}{x}_2+d(t)$, $\frac{d{x}_2}{dt}=k_{21}{x}_1-k_{12}{x}_2$ transformed into $\frac{d{c}_1}{dt}=-(K+k_{21})c_1+\frac{k_{12}{c}_2{V}_2}{V_1}+\frac{d(t)}{V_1}$, $\frac{d{c}_2}{dt}=\frac{k_{21}{V}_1}{V_2}{c}_1-k_{12}{c}_2$ using the relation $c_i=\raisebox{1ex}{$x_i$}\!\left/ \!\raisebox{-1ex}{$V_i$}\right.$

where $c_i(t)$ represents the concentration of the drug (milligrams) in compartment $j,j=1,2$ and

$V_i$ denotes the apparent volume of distribution in the compartment $i$ by using the figure: