Question: 3. Consider the steady state heat on a rectangle bounded by the lines = O, and y = 1, given by 02 u Boundary

3. Consider the steady state heat on a rectangle bounded by the lines = O, and y = 1, given by 02 u Boundary conditions are given by: u(O, y) (a) Show that the solution 02 u Dy2 0) Cn sin (n7rx) sinh (nny) 2 = O. [10 marks] 2 satisfies the boundary conditions u(O, y) = O, = O, and u(x, O) (b) Find the formula for Cn, and calculate the first two coefficients. [15 marks]

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