Chapter 6.1, Problem 10P

Derive the differential equationsfor $x_1(t)$ and $x_2(t)$ in the system $(23)$ by applying the balance law $(22)$ to the compartment model illustrated in Figure $\mathrm{6.1.3}$.

$x_1\text{'}=\left(L+k_{12}{x}_2+k_{13}{x}_3\right)-\left(k_{21}+k_{31}+k_{01}\right)x_1$,

$x_2\text{'}=k_{12}{x}_1-\left(k_{02}+k_{12}\right)x_2$,          $(23)$

$x_3^{\text{'}}=k_{31}{x}_1-k_{13}{x}_3$.

$\frac{dx}{dt}=\text{input}\text{rate}-\text{Output}\text{rate}$,          $(22)$