Question: I just need help getting Cn. Thanks! (10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, 6,u(t,x)

I just need help getting Cn. Thanks!

(10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, 6,u(t,x) = 2632mm x), t e (0, on), x E (0, 5); with initial condition x, x E [0, g), u(0, x) = f(x) = 5 0, x 6 [5,5]. and with boundary conditions u(t,0) = 0, u(t, 5) = 0. Find the solution u using the expansion u(t, 3:) = 2 CH vn(t) w,.(X), n=1 with the normalization conditions a. (3/10) Find the functions w,\" with index n 2 1. w" = sin((npix)/5) 2 b. (3/10) Find the functions 1),, , with index n 2 1. v,l = [eA(-2(npi/5)A2*t) 2 c. (4/10) Find the coefficients c,,, with index n 2 1. c,l = '(2/5)((-5/(npi))cos((npix)/2)+(25/(n'\\2piA2))sin((npix)/2)-1 Z

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