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