EDIT: Typo, the Z' should be Z''
The problem statement sort of suggests that this is a steady state heat transfer problem rather than a transient problem. There is no initial condition.
I have a hunch that is the case since there is no mention of an IC (but I took the assumption that since there is a different T at both ends, there would be an initial T distribution, f(z)).
I am not totally sure though since they didn't explicitly state "steady-state" like they do in other problems.
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