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
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Chapter2: Second-order Linear Odes
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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.
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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