Use MATLAB

Question 1: Apply the Euler method to solve

from to .

Cut and paste the above snippet of code into the MATLAB editor. Modify as necessary and save it as a .m file in order to do the following:

Compute the exact solution and use your program to do the following:

Figure out what is the minimum value of N that you need to get an error smaller than 0.01 at the final time. 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 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 questions.

Here is the code they gave us for a sample problem... we must use the same code just modify it to solve this ODE.