A hand-held calculator will suffice for Problems 1 through 10, where an initial value problem and its exact solution are given. Apply the improved Euler method to approximate this solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing four-decimal-place values of the approximate solution and actual solution at the points = 0.1, 0.2, 0.3, 0.4, 0.5. y'=-3x²y, y(0) = 3; y(x) = 3e-¹
A hand-held calculator will suffice for Problems 1 through 10, where an initial value problem and its exact solution are given. Apply the improved Euler method to approximate this solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing four-decimal-place values of the approximate solution and actual solution at the points = 0.1, 0.2, 0.3, 0.4, 0.5. y'=-3x²y, y(0) = 3; y(x) = 3e-¹
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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Question
![A hand-held calculator will suffice for Problems 1 through 10, where an initial value problem and its exact solution are given. Apply the improved Euler
method to approximate this solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing four-decimal-place values of the
approximate solution and actual solution at the points a = 0.1, 0.2, 0.3, 0.4, 0.5.
y' = -3x²y, y(0) = 3; y(x) = 3e-²
Answer
Note: In Problems 2 through 10, we give the value of x, the corresponding improved Euler value of y, and the true value of y.
0.5, 2.6405, 2.6475](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5779d6d-aa05-4ad7-80c7-ed0d0a2afe0f%2F4686831e-e8f6-492a-9083-ea9057d51e69%2F2novlqb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A hand-held calculator will suffice for Problems 1 through 10, where an initial value problem and its exact solution are given. Apply the improved Euler
method to approximate this solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing four-decimal-place values of the
approximate solution and actual solution at the points a = 0.1, 0.2, 0.3, 0.4, 0.5.
y' = -3x²y, y(0) = 3; y(x) = 3e-²
Answer
Note: In Problems 2 through 10, we give the value of x, the corresponding improved Euler value of y, and the true value of y.
0.5, 2.6405, 2.6475
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