(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) = 5x - 5 and boundary conditions: ди a²u = D at дх2 ди ди (0, t) = 4 -(4,t) = 4 дх дх (a) Determine the steady state temperature distribution: u(x) = 4x (b) Find the full time dependent solution using Fourier series with trigonometric functions chosen appropriately for the boundary conditions. Simplify your answers. -Dwn u(x, t) = A0 + box + Σn ane¯ cos(@nx) + 1 b₁e¯¯ in=1 -Dw sin(@nx) where @n = ? Ao bo = an = F bn =