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(a) Find the general solution in terms of real functions. (b) From the roots of the characteristic equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and classify it as to type. (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = ₁i+2j = yi+y'j of the corresponding dynamical system. Then sketch by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.

(a) Find the general solution in terms of real functions. (b) From the roots of the characteristic equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and classify it as to type. (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = ₁i+2j = yi+y'j of the corresponding dynamical system. Then sketch by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 63EQ
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3- y" - 4y + 4y = 0
Transcribed Image Text:3- y" - 4y + 4y = 0
(a) Find the general solution in terms of real functions. (b) From the roots of the characteristic equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and classify it as to type. (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = £₁i + £2j = yi+y'j of the corresponding dynamical system. Then sketch by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.
Transcribed Image Text:(a) Find the general solution in terms of real functions. (b) From the roots of the characteristic equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and classify it as to type. (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = £₁i + £2j = yi+y'j of the corresponding dynamical system. Then sketch by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.
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