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Statement of a problem № 637

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A rod of length L with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as x = a/T, where a is a constant. The ends of the rod are kept at temperatures T1 and T2. Find the function T(x), where x is the distance from the end whose temperature is T1, and the heat flow density.

Solution:
A rod of length L with thermally insulated lateral surface consists of material

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