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Given the system C. dx dt dx, f. dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie dx dt b. Find eigenpairs. · = x₁ + 2x₂ = Ax. What is A ? Find ¹A. Can you use eigenmethods? No, because there are not enough eigenpairs. Do long way in class, using the associated homogeneous linear differential equation and find its natural fundamental set of solutions associated to time t =0. Then compare it to the formula 4.15 c in the text. d. Give a general solution of the system. e. Give the solution of the IVP with initial value x(0) = 3 Give the solution of the IVP with initial value x(1) =| (3)

Given the system C. dx dt dx, f. dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie dx dt b. Find eigenpairs. · = x₁ + 2x₂ = Ax. What is A ? Find ¹A. Can you use eigenmethods? No, because there are not enough eigenpairs. Do long way in class, using the associated homogeneous linear differential equation and find its natural fundamental set of solutions associated to time t =0. Then compare it to the formula 4.15 c in the text. d. Give a general solution of the system. e. Give the solution of the IVP with initial value x(0) = 3 Give the solution of the IVP with initial value x(1) =| (3)

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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Given the system C. dx, e. dt f. -= 4x₁ - 1x₂ dx₁ a. Write the above system in matrix form ie dx dt b. Find eigenpairs. - = x₁ + 2x₂ dt Ax. What is A ? d. Give a general solution of the system. Give the solution of the IVP with initial value x(0) = (3) Find A. Can you use eigenmethods? No, because there are not enough eigenpairs. Do long way in class, using the associated homogeneous linear differential equation and find its natural fundamental set of solutions associated to time t =0. Then compare it to the formula 4.15 c in the text. Give the solution of the IVP with initial value x(1) =
Transcribed Image Text:Given the system C. dx, e. dt f. -= 4x₁ - 1x₂ dx₁ a. Write the above system in matrix form ie dx dt b. Find eigenpairs. - = x₁ + 2x₂ dt Ax. What is A ? d. Give a general solution of the system. Give the solution of the IVP with initial value x(0) = (3) Find A. Can you use eigenmethods? No, because there are not enough eigenpairs. Do long way in class, using the associated homogeneous linear differential equation and find its natural fundamental set of solutions associated to time t =0. Then compare it to the formula 4.15 c in the text. Give the solution of the IVP with initial value x(1) =
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