4. (-/2 points) DETAILS Classify the critical point (0, 0) of the given linear system by...
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...
(1 point) Classify the critical point (0,0) of the linear 2 x 2 system by computing the trace T, the determinant A and the discriminant D=72 – 4A. xt' = -5x + 3y, y' = 2x – 7y.
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
please show steps. 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.) Conclusion ...Select (X, Y) - ( (x, y) - ( ) ) --Select --Select Slot Need Help? Read it TH
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' = x(1 - x? - 9y2 y' y(9-x -9y?) Conclusion Select ---Select- (x, y) = --- Select (x, y) = -Select- ---Select
(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.
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...
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...
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
(1 point) 2 a. Find the most general real-valued solution to the linear system of differential equations a' -4 -8 21(t) ] =C1 + C2 22(t) 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 preview answers