Problem 2.249

A rod of length $l$ with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as $x=\alpha / T,$ where $\alpha$ is a constant. The ends of the rod are kept at temperatures $T_{1}$ and $T_{2} .$ Find the function $T(x),$ where $x$ is the distance from the end whose temperature is $T_{1},$ and the heat flow density.