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.