Question

Let u be the solution to the initial boundary value problem for the Heat Equation, tE (0, o0), т€ (0, 3)%; дди(t, г) — 4 0?и(t, a), with initial condition E0, , u(0, x) f(x) 3 and with boundary conditions д,u(t, 3) — 0. и(t,0) — 0, Find the solution u using the expansion и(t, 2) 3D У с, чп (t) w,(m), n-1 with the normalization conditions Vn (0) 1, 1. Wn _ (2n 1) a. (3/10) Find the functions wn, with index n> 1 Wn b. (3/10) Find the functions v,n, with index n> 1. c. (4/10) Find the coefficients cn, with index n> 1 W W

Answer 1

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4 Gn Son(2n (2n- 2n- C2n=i) choe Cn) 2n