Question: Please provide all steps. Thank you! Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 20 attempts. (10 points) Let u be the solution to

Please provide all steps. Thank you!

Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 20 attempts. (10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, 0,u(t,x) = 20u(t, x), t E (0, on), x E (0, 5); with initial condition 5 u=f(x>= x, XE [(23), 0' " E [E'Si' and with boundary conditions u(t,0) = 0, 140,5) = 0. Find the solution u using the expansion with the normalization conditions a. (3/10) Find the functions w,\" with index n 2 1. Wu = 2 b. (3/10) Find the functions 1),, , with index n 2 1. Un = Z c. (4/10) Find the coefficients c,\" with index n 2 1. C&quot

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