Finite Difference Approximation

The flux of heat in a metal bar of length 1 is given by the expression q(x) = − k(x + 0.01)dT/dx

If heat is added to the bar along its length with a flux equal everywhere to 0.5, and the temperature at each end is held at some reference temperature,

(a) Find a differential equation for the steady-state temperature profile in the bar with respect to the reference temperature

(b) Derive a finite difference approximation for the differential equation, and write the associated stencil

NB: This needs to be done as soon as possible. No more then 4 hours.