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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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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