Given the initial-value problem y = 2 t y + t 2 et , 1 t 2, y(1) = 0, with exact solution y(t) = t 2(et e): a. Use Taylors method of order two with h = 0.1 to approximate the solution, and compare it with the actual values of y. b. 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 Taylors method of order four with h = 0.1 to approximate the solution, and compare it with the actual values of y. d. 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) 1

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