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Compute the general solution of the system...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral s...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y,
Problem 3. For the...
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c)...
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution dY (1 -2
dY 9. Consider the liner system dt Y. Determine which of the following phase portrait best represents the syste...
dY 9. Consider the liner system dt Y. Determine which of the following phase portrait best represents the system. Justify your answer. Also, compute the general solution. (Sections 3.2, 3.3, and 3.4)
dY 9. Consider the liner system dt Y. Determine which of the following phase portrait best represents the system. Justify your answer. Also, compute the general solution. (Sections 3.2, 3.3, and 3.4)
Problem 6 (3 points) The general solution of the system of the linear system * =...
Problem 6 (3 points) The general solution of the system of the linear system * = AY, Y)= ((0),y(t)), is given below. (1) Sketch the strait- line solutions and the phase portrait. DO NOT forget to use ARROWS. Make sure that your sketch shows ABSOLUTELY CLEAR slopes of Tangent line as t oot -oo. (2) Is the solution stable? Y(t) = kV1 + kye" V2; V. =(2,-1), V, = (1,3)
Consider the following system: dx/dt=y(x^2+y^2-1) dy/dt= -x(x^2 +y^2-1) Find the equilibrium solution. 13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sk...
Consider the following system:
dx/dt=y(x^2+y^2-1)
dy/dt= -x(x^2 +y^2-1)
Find the equilibrium solution.
13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
PROBLEM 3. Suppose that the general solution of a 2-by-2 system x' = Ax is x(t)...
PROBLEM 3. Suppose that the general solution of a 2-by-2 system x' = Ax is x(t) = Cje-t + Czezt, y(t) = 2Cje-t – Cze2t. Sketch the phase portrait of the system and determine the matrix A.
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system...
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system of differential equations dx dt 10x – x2 – 2xy, dy dt 5Y – 3y2 + xy. (a) Determine all of the critical points for the population model. (b) Determine the linearised system for each critical point in part (a) and discuss whether it can be used to approximate the behaviour of the non-linear system. (c) For the critical point at the origin: (i)...
Sketch the phase portrait for each linear system below Y. dt - (33) = (211) dY...
Sketch the phase portrait for each linear system below
Y. dt - (33) = (211) dY dt Y.
diff EQ help??? 0 dY 5. (6 points) Consider the liner system Y. Determine which of...
diff EQ help???
0 dY 5. (6 points) Consider the liner system Y. Determine which of the following dt phase portrait best represents the system. Circle one, or draw a rough sketch to match your choice. Justify your answer.
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine...
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y,
Problem 3. For the...
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution dY (1 -2
dY 9. Consider the liner system dt Y. Determine which of the following phase portrait best represents the system. Justify your answer. Also, compute the general solution. (Sections 3.2, 3.3, and 3.4)
dY 9. Consider the liner system dt Y. Determine which of the following phase portrait best represents the system. Justify your answer. Also, compute the general solution. (Sections 3.2, 3.3, and 3.4)
Problem 6 (3 points) The general solution of the system of the linear system * = AY, Y)= ((0),y(t)), is given below. (1) Sketch the strait- line solutions and the phase portrait. DO NOT forget to use ARROWS. Make sure that your sketch shows ABSOLUTELY CLEAR slopes of Tangent line as t oot -oo. (2) Is the solution stable? Y(t) = kV1 + kye" V2; V. =(2,-1), V, = (1,3)
Consider the following system:
dx/dt=y(x^2+y^2-1)
dy/dt= -x(x^2 +y^2-1)
Find the equilibrium solution.
13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
PROBLEM 3. Suppose that the general solution of a 2-by-2 system x' = Ax is x(t) = Cje-t + Czezt, y(t) = 2Cje-t – Cze2t. Sketch the phase portrait of the system and determine the matrix A.
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system of differential equations dx dt 10x – x2 – 2xy, dy dt 5Y – 3y2 + xy. (a) Determine all of the critical points for the population model. (b) Determine the linearised system for each critical point in part (a) and discuss whether it can be used to approximate the behaviour of the non-linear system. (c) For the critical point at the origin: (i)...
Sketch the phase portrait for each linear system below
Y. dt - (33) = (211) dY dt Y.
diff EQ help???
0 dY 5. (6 points) Consider the liner system Y. Determine which of the following dt phase portrait best represents the system. Circle one, or draw a rough sketch to match your choice. Justify your answer.
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
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