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Use the direction field to determine the stability of the point (0,2). [lmark] 1. .98- 1.96+-...
33 Use the direction field to determine the stability of the point (0, 2). 714 points...
33 Use the direction field to determine the stability of the point (0, 2). 714 points 2.04 References 2.02 2+ 1.98 1.96 x 0.02 0.04 0.06 0.08 0.1 The point (0, 2) is a stable equilibrium point. O The point (0, 2) is an unstable equilibrium point. 7 Select the second-order equation y" + 4xy' + 4y=-9x2 written as a system of first-order equations 714 u'v points -4xv-4u + References u' =4xv+ 4u-9x u'v -4xv-4u-9x2 u'v -4xy-4u + 14 Round...
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...
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field....
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
1. (20 points) Let (a) Determine and plot the equilibrium points and nullclines of the system....
1. (20 points) Let
(a) Determine and plot the equilibrium points and nullclines of
the system.
(b) Show the direction of the vector field between the
nullclines
(c) Sketch some solution curves starting near, but not on, the
equilibrium point(s).
(d) Label each equilibrium point as stable or unstable depending on
the behavior of the
solutions nearby, and describe the long-term behavior of all of the
solutions.
(1 point) The slope field for y' = 0.1(1+y)(3 - y) is shown below P -...
(1 point) The slope field for y' = 0.1(1+y)(3 - y) is shown below P - - --- - On a print out of the slope field, draw solution curves through each of the three marked points (a) As 3 → 00 (As needed, entero in your answers as Inf): For the solution through the top-left point: y → For the solution through the origin: y → For the solution through the bottom-right point: y → (b) What are the...
1. Classify the stability type of the equilibrium point (0,0) of the following linear planar homogeneous...
1. Classify the stability type of the equilibrium point (0,0) of the following linear planar homogeneous systems (same notation as in the previous homework). -(G3) 1 -3 2 -1 A-(25 4 -5
Determine the vector component of this field in the +z direction at point (1,pi/3,5pi/4). 7. A...
Determine the vector component of this field in the +z direction
at point (1,pi/3,5pi/4).
7. A vector field is 3 R +20-6φ . Determine the vector component of this field in the direction at the point (1, 3, 5㎡4). Express the answer in the spherical system.
1. Use Routh criteria to determine the stability of G(s) $*+$3+25+1 2. Use Routh Criteria to...
1. Use Routh criteria to determine the stability of G(s) $*+$3+25+1 2. Use Routh Criteria to determine the values of Kp and Ky such that the negative feedback CLTF is stable, R(S) 1 S3 + S2 + S + 1 X(s) Kp + KDS
Consider the differential equation- (A) At the point (1.5, - 1.5), the direction field has a slop...
Consider the differential equation- (A) At the point (1.5, - 1.5), the direction field has a slope ofPreview (B) At the point (0.5, 1.5), the direction field has a slope of (C) Use your answers above to help choose the corect direction field for the differential equation. Preview :2-1 2 1 11 41 Get help Video Points possible: 1
Consider the differential equation- (A) At the point (1.5, - 1.5), the direction field has a slope ofPreview (B) At the...
5. For the system =1-1-y = 1 - 12 - y2 In a single figure, show...
5. For the system =1-1-y = 1 - 12 - y2 In a single figure, show the following: (a) Determine and plot the equilibrium points and nullclines. (b) Show the direction of the vector field between the nullclines as illustrated in Example 2 and Figure 2.6.3 in the textbook. (c) Sketch some solution curves starting near, but not on, the equilibrium points. (d) Label each equilibrium as stable or unstable depending on the behavior of the solutions that start nearby.
33 Use the direction field to determine the stability of the point (0, 2). 714 points 2.04 References 2.02 2+ 1.98 1.96 x 0.02 0.04 0.06 0.08 0.1 The point (0, 2) is a stable equilibrium point. O The point (0, 2) is an unstable equilibrium point. 7 Select the second-order equation y" + 4xy' + 4y=-9x2 written as a system of first-order equations 714 u'v points -4xv-4u + References u' =4xv+ 4u-9x u'v -4xv-4u-9x2 u'v -4xy-4u + 14 Round...
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...
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
1. (20 points) Let
(a) Determine and plot the equilibrium points and nullclines of
the system.
(b) Show the direction of the vector field between the
nullclines
(c) Sketch some solution curves starting near, but not on, the
equilibrium point(s).
(d) Label each equilibrium point as stable or unstable depending on
the behavior of the
solutions nearby, and describe the long-term behavior of all of the
solutions.
(1 point) The slope field for y' = 0.1(1+y)(3 - y) is shown below P - - --- - On a print out of the slope field, draw solution curves through each of the three marked points (a) As 3 → 00 (As needed, entero in your answers as Inf): For the solution through the top-left point: y → For the solution through the origin: y → For the solution through the bottom-right point: y → (b) What are the...
1. Classify the stability type of the equilibrium point (0,0) of the following linear planar homogeneous systems (same notation as in the previous homework). -(G3) 1 -3 2 -1 A-(25 4 -5
Determine the vector component of this field in the +z direction
at point (1,pi/3,5pi/4).
7. A vector field is 3 R +20-6φ . Determine the vector component of this field in the direction at the point (1, 3, 5㎡4). Express the answer in the spherical system.
1. Use Routh criteria to determine the stability of G(s) $*+$3+25+1 2. Use Routh Criteria to determine the values of Kp and Ky such that the negative feedback CLTF is stable, R(S) 1 S3 + S2 + S + 1 X(s) Kp + KDS
Consider the differential equation- (A) At the point (1.5, - 1.5), the direction field has a slope ofPreview (B) At the point (0.5, 1.5), the direction field has a slope of (C) Use your answers above to help choose the corect direction field for the differential equation. Preview :2-1 2 1 11 41 Get help Video Points possible: 1
Consider the differential equation- (A) At the point (1.5, - 1.5), the direction field has a slope ofPreview (B) At the...
5. For the system =1-1-y = 1 - 12 - y2 In a single figure, show the following: (a) Determine and plot the equilibrium points and nullclines. (b) Show the direction of the vector field between the nullclines as illustrated in Example 2 and Figure 2.6.3 in the textbook. (c) Sketch some solution curves starting near, but not on, the equilibrium points. (d) Label each equilibrium as stable or unstable depending on the behavior of the solutions that start nearby.
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