Let u be the solution to the initial boundary value problem for the Heat Equation, ∂ᵤu(t, x) = 4 ∂²ᵥu(t, x), t ∈ (0, ∞), x ∈ (0, 3); with Neumann boundary conditions ∂ᵥu(t, 0) = 0 and ∂ᵥu(t, 3) = 0 and with initial condition u(0, x) = f(x) = { 3, x ∈ [0, 3/2), 5, x ∈ [3/2, 3]. The solution u of the problem above, with the conventions given in class, has the form u(t, x) = c₀/2 + Σ[n=1,∞] cₙ vₙ(t) wₙ(x), with the normalization conditions vₙ(0) = 1 and wₙ(0) = 1. Find the functions vₙ, wₙ, and the constants c₀ and cₙ for n ≥ 1.