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6. Consider the following system x' = (^2 3)x. (a) Show that the eigenvalues are given...
Consider the spring model x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0...
Consider the spring model
x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0 , we looked at in the previous
problem. Linearize the first-order system that you obtained there
at the third of the critical points you found. [x′y′]=A[xy] [ x ′ y
′ ] = A [ x y ] , where
Consider the spring model x"-8x2x30, we looked at in the previous problem. Linearize the first-order system that you obtained there at the third of...
Math 216 Homework webHW10, Problem 5 Consider the predator/prey model r' = 73 - 22 -...
Math 216 Homework webHW10, Problem 5 Consider the predator/prey model r' = 73 - 22 - ry y = -5y + xy. Find the linearization of this system at the second of the critical points you found in problem 3. , where A = [)] = A ( 3 ) where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "" for V-1. For real answers, enter...
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 *...
Math 216 Homework webHW10, Problem 9 Consider the spring model *" – 1x + 1x2 =...
Math 216 Homework webHW10, Problem 9 Consider the spring model *" – 1x + 1x2 = 0, we looked at in the previous problem. Linearize the first-order system that you obtained there at the second of the critical points you found. [")=[*] where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "i" for V-1. For real answers, enter them in ascending order; for complex, enter 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.
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
The system results from an approximation to the Hodgkin-Huxley equations, which model the transm...
The system results from an approximation to the Hodgkin-Huxley equations, which model the transmission of neural impulses along an axon. (a) Determine all critical points of the given system of equations. [Write your points in ascending order of their x-coordinates.] (___, ___) (___, ___) (___, ___) (b) Classify the critical points by investigating the approximate linear system near each one. **Choose one of the 3 in the () to fill in the blank** The critical point is _______(a saddle, a...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2)...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2) (a) Find the general solution (x(t), y(t) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE (b) Find the solution satisfying the given initial condition (x(6), y(t)) - (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
a. Find the most general real-valued solution to the linear system of differential equations x =...
a. Find the most general real-valued solution to the linear system of differential equations x = -[42]; xid) + c2 x?(༧) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these (1 point) Consider the linear system -6 7-11) -9 15 y. Find the eigenvalues and eigenvectors for the coefficient matrix. 21 = V1 = , and 12...
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...
Consider the spring model
x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0 , we looked at in the previous
problem. Linearize the first-order system that you obtained there
at the third of the critical points you found. [x′y′]=A[xy] [ x ′ y
′ ] = A [ x y ] , where
Consider the spring model x"-8x2x30, we looked at in the previous problem. Linearize the first-order system that you obtained there at the third of...
Math 216 Homework webHW10, Problem 5 Consider the predator/prey model r' = 73 - 22 - ry y = -5y + xy. Find the linearization of this system at the second of the critical points you found in problem 3. , where A = [)] = A ( 3 ) where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "" for V-1. For real answers, enter...
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 *...
Math 216 Homework webHW10, Problem 9 Consider the spring model *" – 1x + 1x2 = 0, we looked at in the previous problem. Linearize the first-order system that you obtained there at the second of the critical points you found. [")=[*] where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "i" for V-1. For real answers, enter them in ascending order; for complex, enter 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.
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. x = 8x + y y' - 2x + 6y. X(O) = (-1,2) (a) Find the general solution (x(t), y(t) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE (b) Find the solution satisfying the given initial condition (x(6), y(t)) - (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
a. Find the most general real-valued solution to the linear system of differential equations x = -[42]; xid) + c2 x?(༧) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these (1 point) Consider the linear system -6 7-11) -9 15 y. Find the eigenvalues and eigenvectors for the coefficient matrix. 21 = V1 = , and 12...
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...
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Please help me with FLOWCHART and UML diagram for class,
thank you!
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