Consider the system of differential equations
Classify the critical point (0,0) as to type and determine whether it is stable, asymptotically stable, or unstable draw several (at least eight) trajectories in the xy-plane.
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Consider the system of differential equations Classify the critical point (0,0) as to type and d...
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)...
At least one of the answers above is NOT correct. (1 point) Consider the differential equation...
At least one of the answers above is NOT correct. (1 point) Consider the differential equation = AX(t) dt where A is a given matrix. Determine whether the equilibrium (0,0) is a stable spiral, an unstable spiral, or a neutral spiral (center). Also determine whether the trajectories travel clockwise or counterclockwise. | 3 91 A = | -16 -5] The equilibrium (0,0) is a stable spiral Trajectories travel counterclockwise The equilibrium (0,0) is a stable spiral Trajectories travel counterclockwise, The...
(6 points) The point (-1,1) is a critical point of the nonlinear system of equations This critical point is a(n) (a...
(6 points) The point (-1,1) is a critical point of the nonlinear system of equations This critical point is a(n) (a) unstable saddle point. (b) asymptotically stable spiral point. (c) unstable node. (d) asymptotically stable proper node / star point.
(6 points) The point (-1,1) is a critical point of the nonlinear system of equations This critical point is a(n) (a) unstable saddle point. (b) asymptotically stable spiral point. (c) unstable node. (d) asymptotically stable proper node / star point.
I'm completely stumped on these. I don't know how to proceed once I get to the...
I'm completely stumped on these. I don't know how to proceed
once I get to the eigenvalue since my typical method for solving
would be to set Ax=x
, then solve. However, this would give me
-5x1=-5x1 and -5x2=-5x2
which makes A trivial. I just realized that means the eigenvectors
will be <1,0> and <0,1>, but I'm still stumped on parts
b and c.
Consider the following system. (A computer algebra system is recommended.) dx = -5 0x dt *...
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.]
4. The origin (0,0) is a critical point of the first order autonomous system x'(t)- Ax(t)...
4. The origin (0,0) is a critical point of the first order autonomous system x'(t)- Ax(t) The origin can classified as asymptotically stable if Re(A) < 0 and stable if Re(A)0 for all eigenvalues λ of A. The origin is unstable if there exists an eigenvalue λ of A where Re(A) >0. For the following systems, classify the origin 1 -3x(C) b, x'(t)=11-3 1-3x(t)
Classify (if possible) each critical point of the given plane autonomous system as a stable node,...
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = xy - 3y - 4 y' = y2 - x2 Conclusion (x, y) =( stable spiral point (x, y) =( unstable spiral point
Consider the following differential equation system: x' = 16x + 8y y = -24x – 12y...
Consider the following differential equation system: x' = 16x + 8y y = -24x – 12y (a) Find the general solution. (b) Without a computer, sketch a phase diagram that shows four linear solution trajectories and that shows one solution trajectory in each of the four regions between the separatrices. (c) Determine the solution that satisfies x(0) = 1 and y(0) = 0. x(t) = yt) = (d) The point (0,0) is a ... Osaddle point stable node unstable node...
Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either...
Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma- separated list. If there are no critical points in a certain category, enter NONE.) dv m = tg - ky dt asymptotically stable VE unstable V mg k х Need Help? Read 1 Talk to a Tutor 2. (-/1 Points] DETAILS ZILLDIFFEQ9...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the syst...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
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)...
At least one of the answers above is NOT correct. (1 point) Consider the differential equation = AX(t) dt where A is a given matrix. Determine whether the equilibrium (0,0) is a stable spiral, an unstable spiral, or a neutral spiral (center). Also determine whether the trajectories travel clockwise or counterclockwise. | 3 91 A = | -16 -5] The equilibrium (0,0) is a stable spiral Trajectories travel counterclockwise The equilibrium (0,0) is a stable spiral Trajectories travel counterclockwise, The...
(6 points) The point (-1,1) is a critical point of the nonlinear system of equations This critical point is a(n) (a) unstable saddle point. (b) asymptotically stable spiral point. (c) unstable node. (d) asymptotically stable proper node / star point.
(6 points) The point (-1,1) is a critical point of the nonlinear system of equations This critical point is a(n) (a) unstable saddle point. (b) asymptotically stable spiral point. (c) unstable node. (d) asymptotically stable proper node / star point.
I'm completely stumped on these. I don't know how to proceed
once I get to the eigenvalue since my typical method for solving
would be to set Ax=x
, then solve. However, this would give me
-5x1=-5x1 and -5x2=-5x2
which makes A trivial. I just realized that means the eigenvectors
will be <1,0> and <0,1>, but I'm still stumped on parts
b and c.
Consider the following system. (A computer algebra system is recommended.) dx = -5 0x dt *...
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.]
4. The origin (0,0) is a critical point of the first order autonomous system x'(t)- Ax(t) The origin can classified as asymptotically stable if Re(A) < 0 and stable if Re(A)0 for all eigenvalues λ of A. The origin is unstable if there exists an eigenvalue λ of A where Re(A) >0. For the following systems, classify the origin 1 -3x(C) b, x'(t)=11-3 1-3x(t)
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = xy - 3y - 4 y' = y2 - x2 Conclusion (x, y) =( stable spiral point (x, y) =( unstable spiral point
Consider the following differential equation system: x' = 16x + 8y y = -24x – 12y (a) Find the general solution. (b) Without a computer, sketch a phase diagram that shows four linear solution trajectories and that shows one solution trajectory in each of the four regions between the separatrices. (c) Determine the solution that satisfies x(0) = 1 and y(0) = 0. x(t) = yt) = (d) The point (0,0) is a ... Osaddle point stable node unstable node...
Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma- separated list. If there are no critical points in a certain category, enter NONE.) dv m = tg - ky dt asymptotically stable VE unstable V mg k х Need Help? Read 1 Talk to a Tutor 2. (-/1 Points] DETAILS ZILLDIFFEQ9...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
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