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7. The system r, = 2(r-1)y. y' = x + y-2, has an equilbrium point at (1,1). This equilibrium point is a(n) (a) unstable node (b) center. (e) saddle (d) unstable focus. 7. The system r, = 2(r...
(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.
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
4. (-/2 points) DETAILS Classify the critical point (0, 0) of the given linear system by...
4. (-/2 points) DETAILS Classify the critical point (0, 0) of the given linear system by computing the tracer and determinant A and using the figure. x - 4x + 3y y' - 2x - 7y A4 Stable spiral 12.44 Unstable spiral Stable node Unstable node 72-44 <0 Center Degenerate stable node Degenerate unstable node Saddle stable spiral degenerate stable node unstable spiral О О О О О О О saddle center stable node unstable node degenerate unstable node
Problem 3: Study the planar system x' = (y – 1)(y – 2), - . Find...
Problem 3: Study the planar system x' = (y – 1)(y – 2), - . Find and sketch the nullclines and give the vectorfield on the nullelines. Also find all steady states and perform a linear stability analysis for each of them to find whether they are stable or unstable and give the type (saddle, node, focus).
Problem 7. (1 point) a. Find the most general real-valued solution to the linear system of...
Problem 7. (1 point) a. Find the most general real-valued solution to the linear system of differential equations X' = [ * ] x1(1) C1 x2(1) + C2 b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses O spiral source spiral sink none of these
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...
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...
Problem 7. (1 point) a. Find the most genera reat valued solution to the inear system...
Problem 7. (1 point) a. Find the most genera reat valued solution to the inear system of diferential equations t' = [": -); x1 (1) = C C + C2 x2 (1) u b. In the phase plane, this system is best described as a source / unstable node sink / stable node O saddle center point / ellipses O spiral source spiral sink none of these
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...
Problem 8. (1 point) 2. Find the most general es-valued solution to the inear system of...
Problem 8. (1 point) 2. Find the most general es-valued solution to the inear system of diferential equations 7' = [-13]: x (1) C + C2 x2 (1) 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 those Problem 9. 11 point) Match each linear system with one of the phase plane direction fields. (The blue lines are...
(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.
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
4. (-/2 points) DETAILS Classify the critical point (0, 0) of the given linear system by computing the tracer and determinant A and using the figure. x - 4x + 3y y' - 2x - 7y A4 Stable spiral 12.44 Unstable spiral Stable node Unstable node 72-44 <0 Center Degenerate stable node Degenerate unstable node Saddle stable spiral degenerate stable node unstable spiral О О О О О О О saddle center stable node unstable node degenerate unstable node
Problem 3: Study the planar system x' = (y – 1)(y – 2), - . Find and sketch the nullclines and give the vectorfield on the nullelines. Also find all steady states and perform a linear stability analysis for each of them to find whether they are stable or unstable and give the type (saddle, node, focus).
Problem 7. (1 point) a. Find the most general real-valued solution to the linear system of differential equations X' = [ * ] x1(1) C1 x2(1) + C2 b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses O spiral source spiral sink none of these
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...
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...
Problem 7. (1 point) a. Find the most genera reat valued solution to the inear system of diferential equations t' = [": -); x1 (1) = C C + C2 x2 (1) u b. In the phase plane, this system is best described as a source / unstable node sink / stable node O saddle center point / ellipses O spiral source spiral sink none of these
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...
Problem 8. (1 point) 2. Find the most general es-valued solution to the inear system of diferential equations 7' = [-13]: x (1) C + C2 x2 (1) 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 those Problem 9. 11 point) Match each linear system with one of the phase plane direction fields. (The blue lines are...
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