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dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase...
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.
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nd the critical points and phase portrait of the given autonomous rst-order differential equation. Classify each critical point as asymptotically stable, unstable, or semi-stable. By hand, sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions(a) dy/dx= y2-y3(b) dy/dx=(y-2)4
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)...
1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general so...
1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general solution to the ODE. (The solution may be expressed in implicit form.)
1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general solution to the ODE. (The solution may be...
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7...
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7 points) Find all critical points and the phase portrait of the autonomous Ist order ODE dy dr -5y+4 Classify each critical point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves in the regions in the ry plane separated by equilibrium solutions. dy dx (S points) Solve the Bernoulli equation:-(- 31-1 7. (8 points) Solve the ODE by variation of parameters: -4y+4y (+...
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...
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...
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and...
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi stable. b) Sketch approximate but clear solutions corresponding to the initial conditions 1.0 -0.8 -0.6 -0.4 0.2 0.2 0.4 0.6 0.8 1.0 -2 .6
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi...
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.]
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.
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)...
1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general solution to the ODE. (The solution may be expressed in implicit form.)
1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general solution to the ODE. (The solution may be...
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7 points) Find all critical points and the phase portrait of the autonomous Ist order ODE dy dr -5y+4 Classify each critical point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves in the regions in the ry plane separated by equilibrium solutions. dy dx (S points) Solve the Bernoulli equation:-(- 31-1 7. (8 points) Solve the ODE by variation of parameters: -4y+4y (+...
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...
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...
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi stable. b) Sketch approximate but clear solutions corresponding to the initial conditions 1.0 -0.8 -0.6 -0.4 0.2 0.2 0.4 0.6 0.8 1.0 -2 .6
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi...
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.]
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.
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