6. y' = −2xy, y(0) = 2; y(x) = 2e−x²
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 answer question 6
![2.6 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 Runge-Kutta method to approximate this solution on
the interval [0, 0.5] with step size h = 0.25. Construct a table
showing five-decimal-place values of the approximate solution
and actual solution at the points x = 0.25 and 0.5.
1. y'= -y, y(0) = 2; y(x) = 2e¯*
2. y' = 2y, y(0) = ½; y(x) = ¹⁄2e²x
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb7f639a-bd7a-4235-8d3a-c185666cdbd7%2F5fd3cf68-2374-4d8a-8ae1-a34f137de1ac%2Fhmz4ypc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.6 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 Runge-Kutta method to approximate this solution on
the interval [0, 0.5] with step size h = 0.25. Construct a table
showing five-decimal-place values of the approximate solution
and actual solution at the points x = 0.25 and 0.5.
1. y'= -y, y(0) = 2; y(x) = 2e¯*
2. y' = 2y, y(0) = ½; y(x) = ¹⁄2e²x
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
