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-x
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-x
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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With the table as said on the question pls
![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) = 1/2; y(x) = ½e²x
3. y' = y + 1, y(0) = 1; y(x) = 2e* - 1
4. y' = x - y, y(0) = 1; y(x) = 2e¯x + x - 1
y'=y-x-1, y(0) = 1; y(x) = 2+x-ex
6. y'= -2xy, y(0) = 2; y(x) = 2e-x²
5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff12ec146-5781-453b-8388-2e7cc9921f6c%2Fb7ed67a0-a43e-46be-8214-bdb55e4a5e9f%2Ftoqcy4_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) = 1/2; y(x) = ½e²x
3. y' = y + 1, y(0) = 1; y(x) = 2e* - 1
4. y' = x - y, y(0) = 1; y(x) = 2e¯x + x - 1
y'=y-x-1, y(0) = 1; y(x) = 2+x-ex
6. y'= -2xy, y(0) = 2; y(x) = 2e-x²
5.
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