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Problem 3. The higher order differential equation and initial conditions are shown as follows: dy dy 2. + y =t+sin(t), y(0) = 0.25, y'(0) = 0.5. dt dt? (a) differential system, including initial conditions. Transform the above initial value problem into an equivalent first order (Ь) form. Express the system in (a) in matrix form, write the initial condition in vector

Problem 3. The higher order differential equation and initial conditions are shown as follows: dy dy 2. + y =t+sin(t), y(0) = 0.25, y'(0) = 0.5. dt dt? (a) differential system, including initial conditions. Transform the above initial value problem into an equivalent first order (Ь) form. Express the system in (a) in matrix form, write the initial condition in vector

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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Problem 3. The higher order differential equation and initial conditions are shown as follows: dy dy + y = t+sin(t), y(0) = 0.25, y (0) = 0.5. dt %3D dt2 (a) differential system, including initial conditions. Transform the above initial value problem into an equivalent first order (b) form. Express the system in (a) in matrix form, write the initial condition in vector (c) Using the second order Runge-Kutta method as follows j; + hF(ti, j;) h T+1 = +(F(t, ÿ;) + F(t+1; y*)). bi+1, to solve system in (b) with step size h, what is the matrix form of the iteration formula? (You do not need to combine the above two equations into one equation)
Transcribed Image Text:Problem 3. The higher order differential equation and initial conditions are shown as follows: dy dy + y = t+sin(t), y(0) = 0.25, y (0) = 0.5. dt %3D dt2 (a) differential system, including initial conditions. Transform the above initial value problem into an equivalent first order (b) form. Express the system in (a) in matrix form, write the initial condition in vector (c) Using the second order Runge-Kutta method as follows j; + hF(ti, j;) h T+1 = +(F(t, ÿ;) + F(t+1; y*)). bi+1, to solve system in (b) with step size h, what is the matrix form of the iteration formula? (You do not need to combine the above two equations into one equation)
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