(1 point) Consider the partial differential equation for heat in a one-dimensional rod with temperature u(x, t): ди Ət 92 D მ2 Assume initial condition: u(x, 0) = 5x and boundary conditions: - 5 Ju მე (0, t) = ди = 4 (4,t) = მე = 4 (a) Determine the steady state temperature distribution: u(x)= (b) Find the full time dependent solution using Fourier series with trigonometric functions chosen appropriately for the boundary conditions. Simplify your answers. -Dw u(x,t) = A₁ + bx +Σae- cos(x) + Σbe sin(x) where wn = n pi/4 Ag= bo an be