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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 unstab¹ nd classify it as to type. (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = x1i+X2j = yi+y'j of the corresponding dynamical system. Then sketen by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories. 1. y" + 2y' - 3y = 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 unstab¹ nd classify it as to type. (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = x1i+X2j = yi+y'j of the corresponding dynamical system. Then sketen by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories. 1. y" + 2y' - 3y = 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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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 unstab¹ nd classify it as to type. □ (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = x₁i + £2j = yi+y'j of the corresponding dynamical system. Then sketen by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories. 1. y" + 2y' - 3y = 0
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 unstab¹ nd classify it as to type. □ (c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = x₁i + £2j = yi+y'j of the corresponding dynamical system. Then sketen by hand, or use a computer, to draw a phase portrait, including any straight-line orbits, from this family of trajectories. 1. y" + 2y' - 3y = 0
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