3. 8 E\\oints total] "This problem involves sofving the ordinary differential equation: dy a Y subject to y(0) =2 a. [2 points] Starting from # = 0, Use Euler's method with 4 = 0.2 and find the solution to the equation up until 7= 1. b. [2 points] Starting from /=0, Use Euler's method with 4 = 0.1 and find the solution to the equation up until 7= 1. c. [2 points] You should be able to write an exact (non-numerical) solution to the equation above. Compare your results from part a. and b. with the exact solution at # = 1. Which value of b gave you the lower etror at # = 1? d. [2 points] Repeat parts a. and b. using Heun's method and report the solutions you find up until /=1 for each step size /= 0.1 and /= 0.2. Plot your results for each part of the problem on the same graph. Remember to label axes and legends appropriately. 4. [4 points] Solve question 3b using the MATLAB command ode45 and add a plot of these results over the range #= 0 to #= 1 on the results you found for question 3. You will need to read the help for this function to complete the question. BONUS [3 points] Repeat question 3 using % = y2. How does your result compare with the analytic solution at t = 1