Find and classify all equilibrium points, draw a phase line, sketch solutions in theyt-plane, and determine whether each equilibrium point is asymptotically stable, semi-stable, or unstable.a. y/ = y ln (y² + )

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Answered: 1 and classify all equilibrium points,…

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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Consider the autonomous equation: P = 0.05P(100 – P)-h, where P is an animal population, and h is the number of animals harvested per unit time. Determine the values of h which yield no equilibrium states, one equilibrium state, and two equilibrium states. (Your responses should involve equalities or inequalities involving h and a real number.) No equilibrium state: One semi-stable equilibrium state: Two distinct equilibrium states:
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=x1i+x2j=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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Populations of owls and mice are modeled by the equations (equations in picture). Answer the following questions. 1. Which of the variables, x or y, represents the owl population and which represents the mice population? Explain. 2. Find the equilibrium solutions and explain their significance.
5_d. Please give step by step solution. Please do part d.
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1 and classify all equilibrium points, draw a phase line, sketch solutions in the lane, and determine whether each equilibrium point is asymptotically stable, semi- le, or unstable.