Your assignment Question 1: Apply the Euler method to solve dy a-a-ty); y(0) = 1 from t-o tot-2 ut and paste the above snippet of code into the MATLAB edrtor. Modify as necessary and save it as a m ile in order to do the following Note that this problem has exact solution uit) 31-1-1 . Figure out what is the minimum value of N that you need to get an error smaller than 0.01 at the final tme. Do this by expenimenting with N until you get a small enough error Plot the computed and exact solution using this value of N Determine rom his computation an approximate time t at which y(t attains its maximum and the approximate maximum value - How many digits of accuracy to you trust in this approximation? - Show the method is approximately second order by doubling N and computing the ratio of the errors. You should hand in a printout of your code, any figures you print, and a report of a few sentences answering all the questons Bonus Question 2 for the brave The Euler method is an example of a first order method. This means that the error is proportional to I so that doubing the number of points The improved Euler method is what's known as a two step method. It requires two evaluations of the function per time step At each st ep, we define two extra quantities before computing Sust Program this method to solve the same problem from Question 1 and . Determine how large N needs to be get an error less than 0.01 - Show the method is second order by doubling N and seeing that the error has gone down by a factor of four Pubisthed with MATLA88 R2017b Your assignment Question 1: Apply the Euler method to solve dy a-a-ty); y(0) = 1 from t-o tot-2 ut and paste the above snippet of code into the MATLAB edrtor. Modify as necessary and save it as a m ile in order to do the following Note that this problem has exact solution uit) 31-1-1 . Figure out what is the minimum value of N that you need to get an error smaller than 0.01 at the final tme. Do this by expenimenting with N until you get a small enough error Plot the computed and exact solution using this value of N Determine rom his computation an approximate time t at which y(t attains its maximum and the approximate maximum value - How many digits of accuracy to you trust in this approximation? - Show the method is approximately second order by doubling N and computing the ratio of the errors. You should hand in a printout of your code, any figures you print, and a report of a few sentences answering all the questons Bonus Question 2 for the brave The Euler method is an example of a first order method. This means that the error is proportional to I so that doubing the number of points The improved Euler method is what's known as a two step method. It requires two evaluations of the function per time step At each st ep, we define two extra quantities before computing Sust Program this method to solve the same problem from Question 1 and . Determine how large N needs to be get an error less than 0.01 - Show the method is second order by doubling N and seeing that the error has gone down by a factor of four Pubisthed with MATLA88 R2017b