(a) Write a function function[u, T] = BackEuler (f, df, a, b, N, ya, maxiter, tol) that implements the Backward Euler method for a scalar differential equation y'(t) = f(t, y). Here, N is the number of steps in the discretization and df refers to the function f_y(t, y). To calculate u_i + 1 at each step, run Newton's method with u_i as the initial guess. Perform at most maxiter number of iterations at each step and terminate early if successive values are less than tol. (b) Solve the combustion model equation y'(t) = y^2(1 - y), 0 lessthanorequalto t lessthanorequalto 2000, y(0) = 0.9 using your code in (a) with maxiter = 20, tol = 10^-12 and N = 5, 10, 20. Plot the results on the same axes