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Apply the standard RK4 method to the following initial value problem: d²y dt² - =- 2t- -1 y(2) = y' (2) = 2 dy + 2y = t³ Int with a step size of h = 0.2. Start by transforming this second order differential equation into a system of first order differential equations by using the variables Ут Y2 = y dy dt Give the approximations w₁ and w₂ of y₁ and y2 in t = 4. Use 16 digits in your calculations and give the answers with at least 5 significant digits w₁ (t = 4) = w₂ (t = 4) =

Apply the standard RK4 method to the following initial value problem: d²y dt² - =- 2t- -1 y(2) = y' (2) = 2 dy + 2y = t³ Int with a step size of h = 0.2. Start by transforming this second order differential equation into a system of first order differential equations by using the variables Ут Y2 = y dy dt Give the approximations w₁ and w₂ of y₁ and y2 in t = 4. Use 16 digits in your calculations and give the answers with at least 5 significant digits w₁ (t = 4) = w₂ (t = 4) =

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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Apply the standard RK4 method to the following initial value problem: d²y dt² - =- 2t- -1 y(2) = y' (2) = 2 dy + 2y = t³ Int with a step size of h = 0.2. Start by transforming this second order differential equation into a system of first order differential equations by using the variables Ут Y2 = y dy dt Give the approximations w₁ and w₂ of y₁ and y2 in t = 4. Use 16 digits in your calculations and give the answers with at least 5 significant digits w₁ (t = 4) = w₂ (t = 4) =
Transcribed Image Text:Apply the standard RK4 method to the following initial value problem: d²y dt² - =- 2t- -1 y(2) = y' (2) = 2 dy + 2y = t³ Int with a step size of h = 0.2. Start by transforming this second order differential equation into a system of first order differential equations by using the variables Ут Y2 = y dy dt Give the approximations w₁ and w₂ of y₁ and y2 in t = 4. Use 16 digits in your calculations and give the answers with at least 5 significant digits w₁ (t = 4) = w₂ (t = 4) =
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