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6. y' = −2xy, y(0) = 2; y(x) = 2e−x²

6. y' = −2xy, y(0) = 2; y(x) = 2e−x²

Advanced Engineering Mathematics
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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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
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
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