kindly solve it using MATLAB

The following differential equation (called the logistic equation) can be used to model a population, y(t). (in thousands) at time t, where t is measured in years: dy =by - ky. dt Here b represents the average birth rate and the death rate at time t is given by ky(t). In what follows, let y(0) = 75+ 25r, b=0.03 and k = 1.5 x 10-3 (where r is your random number). = (a) Using MATLAB and h = 0.25 apply one step of the RK4 method to find y. (b) To find yz, apply one step of the AB2 method (by hand) with h = 0.25. (c) To find yz, apply one step of the AM2 method (by hand) with h = 0.25 and your existing values of y and y2. Clearly state the nonlinear equation for s = y3 that results. To find the value of y3, solve this nonlinear equation to four decimal place accuracy. (Hint: if using the secant method, use initial guesses of so = y and $1 = 42.) (d) To find ys, apply one step of the PC method with AB2 as predictor and AM2 as corrector. (By hand; again, use h=0.25 and your existing values of y, y2 and y.) (e) Find the true solution to the differential equation and state the error in your values of y. 3/2, 43 and ya. () Using the MATLAB ab2 command, solve the problem on the range t (0.1) with 4 and then 8 steps of the AB2 method. Estimate the error at t = 1 using extrapolation and compare the error estimate with the true error. The following differential equation (called the logistic equation) can be used to model a population, y(t). (in thousands) at time t, where t is measured in years: dy =by - ky. dt Here b represents the average birth rate and the death rate at time t is given by ky(t). In what follows, let y(0) = 75+ 25r, b=0.03 and k = 1.5 x 10-3 (where r is your random number). = (a) Using MATLAB and h = 0.25 apply one step of the RK4 method to find y. (b) To find yz, apply one step of the AB2 method (by hand) with h = 0.25. (c) To find yz, apply one step of the AM2 method (by hand) with h = 0.25 and your existing values of y and y2. Clearly state the nonlinear equation for s = y3 that results. To find the value of y3, solve this nonlinear equation to four decimal place accuracy. (Hint: if using the secant method, use initial guesses of so = y and $1 = 42.) (d) To find ys, apply one step of the PC method with AB2 as predictor and AM2 as corrector. (By hand; again, use h=0.25 and your existing values of y, y2 and y.) (e) Find the true solution to the differential equation and state the error in your values of y. 3/2, 43 and ya. () Using the MATLAB ab2 command, solve the problem on the range t (0.1) with 4 and then 8 steps of the AB2 method. Estimate the error at t = 1 using extrapolation and compare the error estimate with the true error