Question 5: (1 point) The temperature u(a:,t) in a bar of length of 8 units obeys the equation @21662u, 00 at 311:2 and we solve the equation by assuming seperation of variables of the form u(:t,t) = F(z) - G(t), for!) g :t S 8, t Z 0. It is easy to see that u(z,t) = 0 for all 1, t is a solution to this partial differential equation, and we are interested in non-trivial solution. The bar has its ends maintained at zero temperature, that is, u(0,t) = Oand u(8,t) = 0 for all t 2 0. Non-trial solution takes the form an = By; sin(%n1rz)e_A'?lt. Enter the expression of An in terms of n and 7r in the box below using Maple syntax. Hence the solution takes the form The initial temperature distribution is u(z,0) = 2sin(7rz)+ % siu(21rz). Calculate the exact values of En as requested below and enter them in the boxes. B8 = 316 = 324 =