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Phase Line Diagrams. Problems
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Differential Equations: An Introduction to Modern Methods and Applications
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- (a) sketch the nullclines, (b) sketch the phase portrait, and () write a brief paragraph describing the possible behaviors of solutions. dx =x(-4x – y + 160) dt dy = y(-x? - y² + 2500) dtarrow_forwardQuestion 4: Linearize i + 2i + 2x? - 12x + 10 = 0. Around its equilibrium positionarrow_forwardFor the following problems: ii. Identify the equilibrium values Construct a phase line. Identify the signs of y' and y". Sketch several solution curves. a. = (y + 2)(y - 3) dx b. = y²-2y dxarrow_forward
- Problems 8 through 13 involve equations of the form dy/dt = f(y). In each problem sketch the graph of f(y) versus y, determine the critical (equilibrium) points, and classify each one as asymptotically stable, unstable, or semistable. Draw the phase line, and sketch several graphs of solutions in the ty-plane.arrow_forward7) In each of the following problems:a. Sketch the Phase Plot of the ODE.b. Determine the equilibrium solutions.c. Classify the equilibrium solutions.d. Draw the phase line and sketch several graphs of solutions on the ty-plane. (7a) y′ = y(y −1)(y −2) , y0 > 0 (7b) y′ = y (1 −y2) , −∞< y0 < ∞. (7c) y′ = y2(1 −y)2, −∞< y0 < ∞. carrow_forward1. Consider the model for population growth below. Use a phase line analysis to sketch solution curves for P(t). Determine if the identified equilibrium is stable or unstable. dP —D P(1 — 2Р) dt 2. Model your own Romeo-Juliet problem. Explain your assumptions and show a plot of the numerical solution. You may add a background story if you want to.arrow_forward
- Question 2. Find the equilibrium solutions of the SIR Model.arrow_forwardPhase Line Diagrams. Problems 1 through 7 involve equations of the form dy/dt = f(y). In each problem, sketch the graph of f(y) versus y, determine the critical (equilibrium) points, and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. 1. dy/dt = y(y - 1)(y-2), yo≥ 0arrow_forward
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