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 1 with the value of y 2 h = 0.1. Compare the three-decimal-place values of the two approximations at x= of the actual solution. y' = y + 3x- 6, y(0) = 2, y(x) = 3 – 3x – e* The Euler approximation whenh=0.25 of y is . (Type an integer or decimal rounded to three decimal places as needed.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
1
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 + 3x - 6, y(0) = 2, y(x) = 3 - 3x - ex
1
The Euler approximation when h = 0.25 of y
is
(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, first with step size h = 0.25, then with step size 1 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 + 3x - 6, y(0) = 2, y(x) = 3 - 3x - ex 1 The Euler approximation when h = 0.25 of y is (Type an integer or decimal rounded to three decimal places as needed.)
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