MY NOTES Let y(x) be the solution of the following initial-value problem. dy + 3x2y = 6x2, y(0) = 7 (a) Use Euler's method and technology to compute y(1) with each of the following step sizes. (i) h = 1 y(1) = 7 (ii) h = 0.1 y(1) = (iii) h = 0.01 y(1) = (iv) h = 0.001 y(1) = (b) Verify that y = 2 + 5e * is the exact solution to the differential equation. We have y = 2 + 5e-x We substitute the values of y and y' and test the solution to see if the left hand side is equal to the right hand side. y' + 3x2y = + 3x2(2 + 5e-x3) = -15x2e-x3 + + 15x2e-x3- C webassign.net/web/Student/Assignment-Responses/last?dep=29934286#Q10 y(1) = (b) Verify that y = 2 + 5e * is the exact solution to the differential equation. We have y = 2+5e-x We substitute the values of y and y' and test the solution to see if the left hand side is equal to the right hand side. y' + 3x2y = + 3 x2 (2 + 5e-*3 ) = -15x2e-x3 + 15x2e-x3 = 6x2 Thus we have, y(0) = 5e-0 = 2 + 5 =7 (c) Find the errors in using Euler's method to compute y(1) with the step sizes in part (a). (Round your 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 valuel = 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 |multiplied by 10 v x (approximately). Need Help? Read it Watch It Viewing Saved Work Revert to Last Response Submit Answer DEC