Question 1: Apply the Euler method to solve dy 8y (t + 1)y2 dt t +1 y(0) = 1 from t = 0 to t = 5. Your code should use a function, just as in the code I used to find z(t) in the most recent section. Modify the above code (using a function f) so that it solves this ODE Note that this problem has exact solution y(t) = 10(t + 1)8 (t + 1)10 + 9 Then do the following: Figure out what is the minimum value of n that you need such that the maximum error is smaller than 0.01. Do this by experimenting with n until you get a small enough error. Plot the computed and exact solution using this value of N. Show the method is approximately first order by doubling n and computing the ratio of the errors. Doing so may require a much larger value of n, especially in the two further questions below. You should find that the solution has exactly one local maximum. y(tmax) Ymax. Use the max function to find approximations to both tmax and YmaxTo do this, you need to call the function with two output arguments. Look at the help for the function max by typing doc max at the Matlab >> prompt. Print out these values and, if possible, plot this point with a marker on your plot of y(t). You should hand in a printout of your code, any figures you print, and a report of a few sentences answering all the questions. Question 1: Apply the Euler method to solve dy 8y (t + 1)y2 dt t +1 y(0) = 1 from t = 0 to t = 5. Your code should use a function, just as in the code I used to find z(t) in the most recent section. Modify the above code (using a function f) so that it solves this ODE Note that this problem has exact solution y(t) = 10(t + 1)8 (t + 1)10 + 9 Then do the following: Figure out what is the minimum value of n that you need such that the maximum error is smaller than 0.01. Do this by experimenting with n until you get a small enough error. Plot the computed and exact solution using this value of N. Show the method is approximately first order by doubling n and computing the ratio of the errors. Doing so may require a much larger value of n, especially in the two further questions below. You should find that the solution has exactly one local maximum. y(tmax) Ymax. Use the max function to find approximations to both tmax and YmaxTo do this, you need to call the function with two output arguments. Look at the help for the function max by typing doc max at the Matlab >> prompt. Print out these values and, if possible, plot this point with a marker on your plot of y(t). You should hand in a printout of your code, any figures you print, and a report of a few sentences answering all the questions