Minnesota gophers in underground burrows must breath, and many have wondered where the $O_2$ come from. One model of these burrows depends on the assumption that it is a long cylinder of radius $R$ located at a short distance $l$ below the surface of the soil. $O_2$ enters the burrow by steady diffusion through the soil; it also steadily diffuses along the burrow's axis to a gopher, who uses $O_2$ at a rate $M.$ Derive equations giving the steady$-$state concentration of $O_2$ as a function of position in the burrow.