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(a) Program a calculator or computer to use Euler's method to compute y(1), where y(x) is the solution of the given initial-value problem. (Give all answers to four decimal places.) dy + 3xy = 15x, y(0) = 6 h = 1 Th = 0.1 Lh = 0.01 h = 0.001 y(1) = 6 y(1) = y(1) = y(1) = (b) Verify that y = 5 + e-* is the exact solution of the differential equation. y = 5 + x3 = LHS = y' + 3xy = + 3x?(5 + e-x) = -3x2e-x3 + + 3x2e-*= 15x2 = RHS y(0) = 1 + e- = 5 + 1 = 6 (c) Find the errors in using Euler's method to compute y(1) with the step sizes in part (a). (Give all answers to four decimal places.) h = 1 error = (exact value - approximate value) = h = 0.1 error = (exact value - approximate value) = h = 0.01 error = (exact value - approximate value) = h = 0.001 error = (exact value - approximate value) = What happens to the error when the step size is divided by 10? When the step size is divided by 10, the error estimate is ---Select--- (approximately). (a) Program a calculator or computer to use Euler's method to compute y(1), where y(x) is the solution of the given initial-value problem. (Give all answers to four decimal places.) dy + 3xy = 15x, y(0) = 6 h = 1 Th = 0.1 Lh = 0.01 h = 0.001 y(1) = 6 y(1) = y(1) = y(1) = (b) Verify that y = 5 + e-* is the exact solution of the differential equation. y = 5 + x3 = LHS = y' + 3xy = + 3x?(5 + e-x) = -3x2e-x3 + + 3x2e-*= 15x2 = RHS y(0) = 1 + e- = 5 + 1 = 6 (c) Find the errors in using Euler's method to compute y(1) with the step sizes in part (a). (Give all answers to four decimal places.) h = 1 error = (exact value - approximate value) = h = 0.1 error = (exact value - approximate value) = h = 0.01 error = (exact value - approximate value) = h = 0.001 error = (exact value - approximate value) = What happens to the error when the step size is divided by 10? When the step size is divided by 10, the error estimate is ---Select--- (approximately)