The temperature u x t in a bar of length of 4 units obeys

Last updated: 3/16/2024

The temperature u x t in a bar of length of 4 units obeys the equation Ju t a u 8x2 0 4 t 0 and we solve the equation by assuming separation of variables of the form u x t F x G t for 0 4 t 0 It is easy to see that u x t 0 for all x t is a solution to this partial differential equation However we are interested in non trivial solutions The bar has its ends maintained at zero temperature that is Non trivial solution takes the form u 0 t 0 and u 4 t 0 for all t 0 un Bn sin n x e Enter the expression of An in terms of n and in the box below using Maple syntax T An Hence the solution takes the form u x t Bn sin Bn sin na et n 1 The initial temperature distribution is u x 0 3 sin x sin 3x Calculate the exact values of Bn as requested below and enter them in the boxes BA Number Bg Number B12 Number