Use MATLAB to code 9. Given the initial-value problem y' = ?y+re', 15152, y(1) = 0, with exact solution y(t) = 12 (e' e): a. Use Taylor's method of order two with h = 0.1 to approximate the solution and compare it with the actual values of y. Use the answers generated in part (a) and linear interpolation to approximate y at the following values and compare them to the actual values of y. i. y(1.04) ii. y(1.55) iii. y(1.97) c. Use Taylor's method of order four with h = 0.1 to approximate the solution and compare it with the actual values of y. Use the answers generated in part (C) and piecewise cubic Hermite interpolation to approximate y at the following values and compare them to the actual values of y. i. y(1.04) ii. y(1.55) iii. y(1.97) Use MATLAB to code 9. Given the initial-value problem y' = ?y+re', 15152, y(1) = 0, with exact solution y(t) = 12 (e' e): a. Use Taylor's method of order two with h = 0.1 to approximate the solution and compare it with the actual values of y. Use the answers generated in part (a) and linear interpolation to approximate y at the following values and compare them to the actual values of y. i. y(1.04) ii. y(1.55) iii. y(1.97) c. Use Taylor's method of order four with h = 0.1 to approximate the solution and compare it with the actual values of y. Use the answers generated in part (C) and piecewise cubic Hermite interpolation to approximate y at the following values and compare them to the actual values of y. i. y(1.04) ii. y(1.55) iii. y(1.97)