Question: It is shown in physics that the temperature u(x,t) at time t at the point x of a long, insulate rod that lies along the x-axis satisfies the one-dimensional heat equation: du/dt = k (d ² u/dx ² ) where k is a constant. Show that the function u = u(x,t) = exp(-n ² kt)sin(nx) satisfies the one-dimensional heat equation for any choice of the constant n.

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