Question: Please provide all steps. Thank you! (10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, 6,u(t, x)

Please provide all steps. Thank you!

(10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, 6,u(t, x) = 4612mm x), t e (0, co), x e (0, 5); with initial condition 1, x E [0, g), u(0, X) = f(X) = 5 2, x E [5, 5] . and with boundary conditions 0xu(t,0) = 0, 0xu(t, 5) = 0. Find the solution 14 using the expansion c co _ _0 u(t,x) 2 + ; cu vn(t) wn(x), with the normalization conditions vn(0) = 1, wn(0) = 1. a. (3/10) Find the functions u)\

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