HELP with finite element homework

[MadisonXY]

Homework Statement

Two ends of a bar of length L are held at temperatures To and TL at positions x=o and x=L, respectively. Thermal conductivity k(x)= Ko/(1+ x/L) , ko is a constant.
cross section of the bar is uniform and longs sides are thermally insulated, there's no source of heat within the bar.

a. what differential relation describes the temperature as a function of position in the bar
b. Solve the system for temperature distribution, T(x), in terms of To, TL, L and Ko

Homework Equations

-Dq+Q=0 q=-deltaT
Not sure...

The Attempt at a Solution

This is a HW from finite element course. I really don't know how to start with k is nonuniform.

 

[AvroArrow]

for a. I think it should be something like dq/dx -Q=0. But I am not sure. I really appreciate if someone can give some hints or solutions. Thanks in advance.