(1 point) Consider the partial differential equation for heat in a one-dimensional rod with temperature u(x,t): Assume initial condition: u(x, 0) 7+4.25 and boundary conditions: ди Ət J²u 922 = u(0,t) 7 u(4,t) = 20 (a) Determine the steady state temperature distribution: u(x) = 7+(13x/4) (b) Find the full time dependent solution using Fourier series with trigonometric functions chosen appropriately for the boundary conditions. Simplify your answers. D u(x,t) cos() +Σue = Ag+box+ae- 16 16 ˙sin() Ap = 7 = (13/4) bo an bn = 0 = -cos(npi)/(2npi)