6. y'= -2xy, y(0) = 2; y(x) = 2e-x² 2x3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve question 6
![2.5 Problems
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 solu-
tion and actual solution at the points x = 0.1, 0.2, 0.3, 0.4,
0.5.
1. y' = -y, y(0) = 2; y(x) = 2e¯*
2. y' = 2y, y(0) = ⁄⁄; y(x) = ½ e²x
3. y' = y + 1, y(0) = 1; y(x) = 2ex - 1
-
4. y' = x - y, y(0) = 1; y(x) = 2e¯x + x − 1
5. y' = y - x - 1, y(0) = 1; y(x) = 2 + x − ex
6. y' = −2xy, y(0) = 2; y(x) = 2e¯x²
y'=-3x² y, y(0) = 3; y(x) = 3e
7.
-x3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb7f639a-bd7a-4235-8d3a-c185666cdbd7%2Fa2587ce9-690e-451f-800d-15ac2072bb9a%2Fgfixt2j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.5 Problems
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 solu-
tion and actual solution at the points x = 0.1, 0.2, 0.3, 0.4,
0.5.
1. y' = -y, y(0) = 2; y(x) = 2e¯*
2. y' = 2y, y(0) = ⁄⁄; y(x) = ½ e²x
3. y' = y + 1, y(0) = 1; y(x) = 2ex - 1
-
4. y' = x - y, y(0) = 1; y(x) = 2e¯x + x − 1
5. y' = y - x - 1, y(0) = 1; y(x) = 2 + x − ex
6. y' = −2xy, y(0) = 2; y(x) = 2e¯x²
y'=-3x² y, y(0) = 3; y(x) = 3e
7.
-x3
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