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1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and...
Problem RMTE1.2 The left panel represents the graph of f(y), the right-hand-side of the differential equation/(). Sketc...
Problem RMTE1.2 The left panel represents the graph of f(y), the right-hand-side of the differential equation/(). Sketch the solutions on the right panel and determine the dt nature of the equilibrium points 0.4 2.0 0.2 1.6 y1 1.2 0.0 0.8 0.2 0.4 0.0 -0.4 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 (a)Y1 asymptotically stable; y2 unstable (c) yi-unstable; y2 semi-s (b) yi asymptotically stable; y2 semi-stable able (d) yi-unstable; y2 asymptotically stable...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
For the equation (dp/dt)=(P+2)(P^2-6P+5) find the equilibrium points and make a phase portrait of the differential...
For the equation (dp/dt)=(P+2)(P^2-6P+5) find the equilibrium points and make a phase portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions.
+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential...
+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential equation y y 2.0 1.5 1.0 0.5 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.6 (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y(0) 0 (iii y(0) 1 (ii) y(0) 0.5 (iv) y(0) 1.6 V y 2:0 1.5 1.5 .5 X -0.6 O-0.6 -0.2 -0.4 0.6 -0.4 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 2.0r 1.5 1.5 0.5...
dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase...
dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase dt portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions. (6pts)
Using Differential Equations. 6. For y, = y3 _ y, y(0) = 30, -00 <30 <...
Using Differential
Equations.
6. For y, = y3 _ y, y(0) = 30, -00 <30 < 00, draw the graph of (y) = y3-y versus y, determine the equilibrium solutions (critical points) and classify each one as unstable or asymptotically stable. Draw the phase line, and sketch several representative integral curves (graphs of solutions) in the (t, y) plane. Hint: None of this requires explicit formulas for solutions y = φ(t) of the initial value problem.]
Consider the autonomous first-order differential equation y = 10 + 3y – v2 Find the DISTINCT...
Consider the autonomous first-order differential equation y = 10 + 3y – v2 Find the DISTINCT critical points and classify each as (1) AS for Asymptotically Stable, (2) US for Unstable or (3) SS for Semi-Stable. Enter your answer as a comma separated list of pairs consisting on a critical point and its stability type (e.g. your answer might look like (2,AS), (-3,SS), (7,US)) Critical Point and Stability: For the initial value problem y' = 10 + 3y – y,...
1. (10 points) Consider the autonomous equation dy = y2 + 3y + 2 dc (a)...
1. (10 points) Consider the autonomous equation dy = y2 + 3y + 2 dc (a) (6 points) Determine the equilibrium solutions of the equation, and classify each as asymptotically stable or unstable. (b) (4 points) Sketch at least three solutions to the equation, choosing initial points not corresponding to the equilibrium solutions. Include the equilibrium solutions in your sketch.
MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following autonomous first-order differential equation. dy =...
MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following autonomous first-order differential equation. dy = y219 - y2) Find the critical points and phase portrait of the given differential equation. dx 6 3 3 0 0 ol -6 -6 -3 Classify 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 critical points in a certain category, enter NONE.) asymptotically stable...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential equation Y" + 2y' + y = 0. From the system, find all equilibrium solutions, and determine if each equilibrium solution is asymptotically stable, or unstable.
Problem RMTE1.2 The left panel represents the graph of f(y), the right-hand-side of the differential equation/(). Sketch the solutions on the right panel and determine the dt nature of the equilibrium points 0.4 2.0 0.2 1.6 y1 1.2 0.0 0.8 0.2 0.4 0.0 -0.4 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 (a)Y1 asymptotically stable; y2 unstable (c) yi-unstable; y2 semi-s (b) yi asymptotically stable; y2 semi-stable able (d) yi-unstable; y2 asymptotically stable...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential equation y y 2.0 1.5 1.0 0.5 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.6 (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y(0) 0 (iii y(0) 1 (ii) y(0) 0.5 (iv) y(0) 1.6 V y 2:0 1.5 1.5 .5 X -0.6 O-0.6 -0.2 -0.4 0.6 -0.4 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 2.0r 1.5 1.5 0.5...
dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase dt portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions. (6pts)
Using Differential
Equations.
6. For y, = y3 _ y, y(0) = 30, -00 <30 < 00, draw the graph of (y) = y3-y versus y, determine the equilibrium solutions (critical points) and classify each one as unstable or asymptotically stable. Draw the phase line, and sketch several representative integral curves (graphs of solutions) in the (t, y) plane. Hint: None of this requires explicit formulas for solutions y = φ(t) of the initial value problem.]
Consider the autonomous first-order differential equation y = 10 + 3y – v2 Find the DISTINCT critical points and classify each as (1) AS for Asymptotically Stable, (2) US for Unstable or (3) SS for Semi-Stable. Enter your answer as a comma separated list of pairs consisting on a critical point and its stability type (e.g. your answer might look like (2,AS), (-3,SS), (7,US)) Critical Point and Stability: For the initial value problem y' = 10 + 3y – y,...
1. (10 points) Consider the autonomous equation dy = y2 + 3y + 2 dc (a) (6 points) Determine the equilibrium solutions of the equation, and classify each as asymptotically stable or unstable. (b) (4 points) Sketch at least three solutions to the equation, choosing initial points not corresponding to the equilibrium solutions. Include the equilibrium solutions in your sketch.
MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following autonomous first-order differential equation. dy = y219 - y2) Find the critical points and phase portrait of the given differential equation. dx 6 3 3 0 0 ol -6 -6 -3 Classify 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 critical points in a certain category, enter NONE.) asymptotically stable...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential equation Y" + 2y' + y = 0. From the system, find all equilibrium solutions, and determine if each equilibrium solution is asymptotically stable, or unstable.
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