(1 point) Classify the critical point (0,0) of the linear 2 x 2 system by computing...
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
Classify the critical point (0, 0) of the given linear system. Draw a phase portrait. dx/df 3x+ y a. dx/dt -x+ 2y dx/dt =-x +3y dy/dt -2x + y dy/dt x+ y Classify the stationary point (0, 0) of the given linear system. Draw a phase portrait. dy/dt -x+y b. dx/dt =-2x-y dx/dt-2x +5/7 y dx/dt 3x-y dx/dt 3x dy/dt 3x- y dy/dt 7x- 3y dy/dt x+y dy/dt 3y
Consider an autonomous system , = (1 + c)x + cy where c is a real constant. (a) Calculate the trace T and the determinant of the coefficient matrix c+1 c (b) For each following cases of c, classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). Note that if a critical point is a center, it is stablhe. (4) c=흘 (2) c=-2 (1) c=-1 (3) c=-8
Consider an autonomous...
3. Consider an autonomous system z'=cx +2y where c is a real constant. 2 (a) Calculate the trace T and the determinant A of the coefficient matrix -2 1 (b) For each following cases of c, classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). Note that if a critical point is a center, it is stable. (1) c--5 (2) c--3 (3) c1 (4) c 6
3. Consider an autonomous...
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)
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. 5 0 -5 5 0 -5
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
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
Problem 4. (1 point) Find the solution to the linear system of differential equations 5x -8y 4x - 7y satisfying the initial conditions x(0) = 6 and y(0) = 4. x(1)
Name Date Period Kuta Software Solving Systems of Equations by Substitution Solve each system by substitution. 1) y=6x-11 2) 2x - 3y = -1 -2x - 3y =-7 y=x-1 3) y=-3x + 5 5x - 4y=-3 4) -3x – 3y = 3 y=-5x-17 5) y=-2 4x - 3y = 18 6) y = 5x - 7 -3x - 2y=-12 7) y=-3x - 19 5x + 8y = 0 8) y = 5x - 3 -x + 7y=-21