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) Find the general solution in terms of real functions. From the roots of the characteristic equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and ssify it as to type. Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = ₁i+x2j = yi+y'j of the corresponding dynamical system. Then sketch by nd, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.

) Find the general solution in terms of real functions. From the roots of the characteristic equation, determine whether each critical point of the corresponding dynamical system is asymptotically stable, stable, or unstable, and ssify it as to type. Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = ₁i+x2j = yi+y'j of the corresponding dynamical system. Then sketch by nd, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 31E
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21. y" + 4y + 4y = 0
Transcribed Image Text:21. 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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