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 1 X= with the value of y (1) 2 y' = -3x²y, y(0) = 9, y(x)=9e -x³ of the actual solution. The Euler approximation when h=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
Publisher:Erwin Kreyszig
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 h = 0.1. Compare the three-decimal-place values of the two approximations at
1
(1)
2
y' = -3x²y, y(0) = 9, y(x) = 9e -x³
X= with the value of y
of the actual solution.
***
The Euler approximation when h = 0.25 of y (1) ₁
(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 h = 0.1. Compare the three-decimal-place values of the two approximations at 1 (1) 2 y' = -3x²y, y(0) = 9, y(x) = 9e -x³ X= with the value of y of the actual solution. *** The Euler approximation when h = 0.25 of y (1) ₁ (Type an integer or decimal rounded to three decimal places as needed.)
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