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Apply Euler's method twice to approximate the solution to the initial value problem on the interval 0,- , first with step size h = 0.25, then with step size h = 0.1. Compare the three-decimal-place values of the two approximations at x = with the value of y of the actual solution. y' =y - 4x + 1, y(0) = 2, y(x) = 3 + 4x - e* The Euler approximation when h = 0.25 of y is 3.438. (Type an integer or decimal rounded to three decimal places as needed.) The Euler approximation when h = 0.1 of y is 3.389'. (Type an integer or decimal rounded to three decimal places as needed.) The value of 2 using the actual solution is 3.351. (Type an integer or decimal rounded to three decimal places as needed.) The approximation 3.389 , using the lesser value of h, is closer to the value of y found using the actual solution. (Type an integer or decimal rounded to three decimal places as needed.)

Apply Euler's method twice to approximate the solution to the initial value problem on the interval 0,- , first with step size h = 0.25, then with step size h = 0.1. Compare the three-decimal-place values of the two approximations at x = with the value of y of the actual solution. y' =y - 4x + 1, y(0) = 2, y(x) = 3 + 4x - e* The Euler approximation when h = 0.25 of y is 3.438. (Type an integer or decimal rounded to three decimal places as needed.) The Euler approximation when h = 0.1 of y is 3.389'. (Type an integer or decimal rounded to three decimal places as needed.) The value of 2 using the actual solution is 3.351. (Type an integer or decimal rounded to three decimal places as needed.) The approximation 3.389 , using the lesser value of h, is closer to the value of y found using the actual solution. (Type an integer or decimal rounded to three decimal places as needed.)

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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Apply Euler's method twice to approximate the solution to the initial value problem on the interval 0, 1 first with step size h = 0.25, then with step size h = 0.1. Compare the three-decimal-place values of the two 1 with the value of y 2 approximations at x = of the actual solution. у' -у-4x+1, у(0) %3D2, у(x) %3 3 +4x - е The Euler approximation when h = 0.25 of y 1 is 3.438'. (Type an integer or decimal rounded to three decimal places as needed.) The Euler approximation when h = 0.1 of y is 3.389. 2 (Type an integer or decimal rounded to three decimal places as needed.) The value of y using the actual solution is 3.351 (Type an integer or decimal rounded to three decimal places as needed.) 1 The approximation 3.389 , using the lesser value of h, is closer to the value of y found using the actual solution. 2 (Type an integer or decimal rounded to three decimal places as needed.)
Transcribed Image Text:Apply Euler's method twice to approximate the solution to the initial value problem on the interval 0, 1 first with step size h = 0.25, then with step size h = 0.1. Compare the three-decimal-place values of the two 1 with the value of y 2 approximations at x = of the actual solution. у' -у-4x+1, у(0) %3D2, у(x) %3 3 +4x - е The Euler approximation when h = 0.25 of y 1 is 3.438'. (Type an integer or decimal rounded to three decimal places as needed.) The Euler approximation when h = 0.1 of y is 3.389. 2 (Type an integer or decimal rounded to three decimal places as needed.) The value of y using the actual solution is 3.351 (Type an integer or decimal rounded to three decimal places as needed.) 1 The approximation 3.389 , using the lesser value of h, is closer to the value of y found using the actual solution. 2 (Type an integer or decimal rounded to three decimal places as needed.)
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