Concept explainers
Heat equation The flow of hear along a thin conducting bar is governed by the one-dimensional heal equation (with analogs for thin plates in two dimensions and for solids in three dimensions)
where u is a measure of the temperature at a location x on the bar at time t and the positive constant k is related to the conductivity of the material. Show that the following functions satisfy the heal equation with k = 1.
84. u(x, t) = 10e–t sin x
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