(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.
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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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.
Transcribed Image Text:5- y" - 2y + 2y = 0
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