a) Transform the second order ODE with independent variable z, dy - 6 dr + 5y = 0, into a dynamical system of first-order ODES with independent variable t. b) Find the corresponding eigenvalues and eigenvectors of the dynamical system of first order ODE obtained in a) and write down the general solution of this system of ODES. c)Solve directly the 2nd-order ODE defined in a) providing its general solution. Compare this general solution with the general solution of the dynamical system of ODES obtained in b). Explain why they are equivalent.

a) Transform the second order ODE with independent variable z, dy - 6 dr + 5y = 0, into a dynamical system of first-order ODES with independent variable t. b) Find the corresponding eigenvalues and eigenvectors of the dynamical system of first order ODE obtained in a) and write down the general solution of this system of ODES. c)Solve directly the 2nd-order ODE defined in a) providing its general solution. Compare this general solution with the general solution of the dynamical system of ODES obtained in b). Explain why they are equivalent.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 35EQ

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