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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 + 3x²y = 6x²;y(0) = 3. Use dx = i) 1, ii) 0.1, ii) 0.01, and, iv) 0.005. Note each of i, ii, iii, and iv increases the 4. 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 + 3x²y = 6x²;y(0) = 3. Use dx = i) 1, ii) 0.1, ii) 0.01, and, iv) 0.005. Note each of i, ii, iii, and iv increases the 4. 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. 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, ii) 0.01, and, iv) 0.005. Note each of i, ii, iii, 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.
Transcribed Image Text:4. 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, ii) 0.01, and, iv) 0.005. Note each of i, ii, iii, 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.
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