The two-dimensional heat equation for an insulated thin plate is: du/dt = k (d2u/dx^2 + d2u/dy2) . S
Question: The two-dimensional heat equation for an insulated thin plate is: du/dt = k (d2u/dx2 + d2u/dy2) . Show that the function u = u(x,y,t) = exp (-[m2 +n2]kt)sin(mx)cos(ny) satisfies this equation for any choice of the constants m and n.
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