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Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: dy * + 3x?y = 6x²;y(0) = 3. Use dx = i) 1, ii) 0.1, iii 0.01, and, iv) 0.005. Note each of i, ii, ii, and iv increases the dx number of iterations by a factor of 10. A computer program would be helpful (see link in resources) b) Determine the exact solution (show your work), and c) find the error in Euler's method to compute y(1) and make a conjecture ton what happens to the error as the step size is divided by 10.

Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: dy * + 3x?y = 6x²;y(0) = 3. Use dx = i) 1, ii) 0.1, iii 0.01, and, iv) 0.005. Note each of i, ii, ii, and iv increases the dx number of iterations by a factor of 10. A computer program would be helpful (see link in resources) b) Determine the exact solution (show your work), and c) find the error in Euler's method to compute y(1) and make a conjecture ton what happens to the error as the step size is divided by 10.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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#4: Please answer A&B

Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: + 3x2y = 6x2; y(0) = 3. Use dx = i) 1, ii) 0.1, iii) 0.01, and, iv) 0.005. Note each of i, ii, iii, and iv increases the 4. dy dx number of iterations by a factor of 10. A computer program would be helpful (see link in resources) b) Determine the exact solution (show your work), and c) find the error in Euler's method to compute y(1) and make a conjecture ton what happens to the error as the step size is divided by 10.
Transcribed Image Text:Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: + 3x2y = 6x2; y(0) = 3. Use dx = i) 1, ii) 0.1, iii) 0.01, and, iv) 0.005. Note each of i, ii, iii, and iv increases the 4. dy dx number of iterations by a factor of 10. A computer program would be helpful (see link in resources) b) Determine the exact solution (show your work), and c) find the error in Euler's method to compute y(1) and make a conjecture ton what happens to the error as the step size is divided by 10.
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