Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 7. The analytic...

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Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 7. The analytic solution is 2. 56 y(x) %=Dㅎ + x e-3(x - 1). %3D 9. (a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method is used. (b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5). (Proceed as in Example 1 of Section 6.1.) (c) Approximate y(1.5) using h = 0.1 and h = 0.05 with Euler's method. See Problem 1 in Exercises 2.6. (Round your answers to four decimal places.) h = 0.1 y(1.5) x h = 0.05 y(1.5) x (d) Calculate the errors in part (c) and verify that the global truncation error of Euler's method is O(h). (Round your answers to four decimal places.) Since y(1.5) = the error for h 0.1 is Eo.1 = L while the error for h = 0.05 is Eo.05 = With global truncation error 0(h) we expect Eo.1/Eo.05 x 2. We actually have Eo.1/Eo.05 = (rounded to two decimal places). Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 7. The analytic solution is 2. 56 y(x) %=Dㅎ + x e-3(x - 1). %3D 9. (a) Find a formula involving c and h for the local truncation error in the nth step if Euler's method is used. (b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5). (Proceed as in Example 1 of Section 6.1.) (c) Approximate y(1.5) using h = 0.1 and h = 0.05 with Euler's method. See Problem 1 in Exercises 2.6. (Round your answers to four decimal places.) h = 0.1 y(1.5) x h = 0.05 y(1.5) x (d) Calculate the errors in part (c) and verify that the global truncation error of Euler's method is O(h). (Round your answers to four decimal places.) Since y(1.5) = the error for h 0.1 is Eo.1 = L while the error for h = 0.05 is Eo.05 = With global truncation error 0(h) we expect Eo.1/Eo.05 x 2. We actually have Eo.1/Eo.05 = (rounded to two decimal places).