As described in Sec. 9.5, linear algebraic equations can arise in the solution of differential equations. The following differential equation results from a steady-state mass balance for a chemical in a one-dimensional canal, 0 = D d²c U dc - kc dx² dx where x = distance along the canal (m), c = concentration, t = time, x = distance, D = diffusion coefficient, U = fluid velocity, and k = a first-order decay rate. (a) Convert this differential equation to an equivalent system of simultaneous algebraic equations using centered difference approximations for the derivatives. (b) Develop a function to solve these equations from x = 0 to L and return the resulting distances and concentrations. The first line of your function should be function [x, c] = YourLastName_reactor(D, U, k, CO, CL, L, dx) (c) Develop a script that invokes this function and then plots the results. (d) Test your script for the following parameters: L = 10 m, Ax = 0.5 m, D= 2 m²/d, U = 1 m/d, k = 0.2/d, c(0) = 80 mg/L, and c(10) = 20 mg/L.