a$)$ Consider a compartmental system with two compartments, A and $B,$

where the rate of transfer from compartment $A$ to $B$ is proportional

to the amount in A with rate constant $k_1,$ and the rate of transfer

from $B$ to $A$ is proportional to the amount in $B$ with rate constant $k_2.$

Derive the system of first$-$order linear differential equations governing

the amounts $x_A(t)$ and $x_B(t)$ in compartments A and $B,$ respectively.