Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.0-2사-2-2 Consider the following autonomous first-order differential equation.Find the critical points and phase portrait of the given differential equation.asymptotically stableClassify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability. Enter your answers as a comma-separated list. If there are no criticalpoints in a certain category, enter NONE.)unstableasymptotically stable00Classify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability. Enter your answers as a comma-separated list. If there are no criticalpoints in a certain category, enter NONE.)unstableOFsemi-stableSketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.

The given autonomous first order differential equation is , dydx = y2-2y The critical…

Answered: Consider the following autonomous…

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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I. Classify each differential equations in terms of order, degree, dependent variable,independent variable, ordinary or partial, and linear or non-linear. If non-linear, state theterm where it is non-linear.
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A. State the order of the differential equation and determine whether the equation is linear or nonlinear.
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Use a computer system or graphing calculator to plot a slope field and/or enough solution curves to indicate whether each critical point of the given differential equation is stable, unstable, or semistable (2-4) Identify any semistable critical point(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The differential equation has semistable critical point(s) at x= (Simplify your answer. Use a comma to separate answers as needed.) O B. The differential equation has no semistable citical points.
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A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2014 can be modeled by y = 320.110/1+377e-0.257t 320,110 1 + 377e−0.257t where t represents the year, with t = 5 corresponding to 1985. (a) Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006. (Round your answers to the nearest whole number.) 1998 y = cell sites 2003 y = cell sites 2006 y = cell sites (b) Use a graphing utility to graph the function. (c) Use the graph to determine the year in which the number of cell sites reached 280,000. The number of cell sites reached 280,000 in . (d) Confirm your answer to part (c) algebraically. The number of cell sites reached 280,000 in .
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