5. Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at temperature zero. If the linear law of heat transfer applies, then the heat equation takes on the form k d²u dx² hu = ди at' 0 0, h a constant. Find the temperature u(x, t) if the initial temperature is f(x) throughout and the ends x = 0 and x = L are insulated. See Figure 12.3.3. insulated 0° insulated L X 0° heat transfer from lateral surface of the rod

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