(5 points) Solve the heat problem with non-homogeneous boundary conditions ди J²u -(x,t) = (x,t), 0 < x < 1, t>0 дх² u(x, t)dx = 0, t> 0, ux (0,t) = 1, ux (1,t) = 1, t> 0, u(x, 0) = 0, 0 < x < 1. Recall that we find h(x), set u(x,t) = u(x, t) - h(x), solve a heat problem for u(x, t) and write u(x, t) = v(x,t) + h(x). Find h(x) h(x) = The solution u(x, t) can be written as The solution u(x, t) can be written as u(x,t) = h(x) + v(x, t), where v(x,t) = Σ Finally, find IM8 n=1 lim u(x,t) = | 8011 ∞ v(x,t) = Σ an e²nt n(x) n=1