Students Home X Content X A MTH 125 Lesson 9.2 - X Watch It Player | Ceng X O Euler's method(1st-de X C A)Program A Calculat X G how to take a screens X + C webassign.net/web/Student/Assignment-Responses/submit? dep=27399747&tags=autosave#question4918976_8 Update : 10. [1/ 15 POINTS] DETAILS PREVIOUS ANSWERS SCALLETY y.4.UZO. IVIT NOTES ASK YOUR ICACHER PRACTICE ANOTHER Let y(x) be the solution of the following initial-value problem. dx dy + 3x2y = 18x2, 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 X (ii) h = 0.1 y(1) = X (iii) h = 0.01 y(1) = X (iv) h = 0.001 y(1) = X (b) Verify that y = 6 + e-x is the exact solution to the differential equation. We have y =6+exs y' 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(6 + e -x5) X = -3x2e-x3 + + 3x2e-x3 X = 18x2 Thus we have, y(0) = +e = 6 +1 =7 XStudents Home X Content X A MTH 125 Lesson 9.2 - X Watch It Player | Ceng X O Euler's method(1st-de x C A)Program A Calculat X G how to take a screens X + C webassign.net/web/Student/Assignment-Responses/submit?dep=27399747&tags=autosave#question4918976_8 G Update : 1 .. y(1) = X (iii) h = 0.01 y(1) = X (iv) h = 0.001 y(1) = X (b) Verify that y = 6 + e-x ; is the exact solution to the differential equation. We have y =6+exs = y' 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 = + 3x-(6 + e-x's) X = -3x2e-x" + + 3x2e-x3 X = 18x2 Thus we have, y(0) = +e= 6 +1 = 7 X (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| = X 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 |divided by 10 v (approximately). Need Help? Read It Watch It