Consider a uniform bar such that α(x) = 1, β(x) = 0.5 with q(x) = x(1 - x). The bar is subject to a constant temperature at x= 0 and is insulated at x= 1 such that θ(0) = 0, dθ/dx (1) = 0. Let S be the vector space which is the intersection of P3[0,1] with the subspace of C[0,1] of all functions satisfying the homogeneous boundary conditions. Find the best least squares approximation for the temperature distribution in the bar from S.