Homework Answers
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
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show at eq. point (4,0) the Jacobian matrix is -4 -8 0 1 f) draw phase portrait near (4,0) from (d) g) at eq. point (2,1) the Jacobian matrix is -2 -4 0.5 0 h) draw phase portrait near (2,1) from (f) i)...
Please solve this in Matlab Consider the initial value problem dx -2x+y dt x(0) m, y(0)...
Please solve this in Matlab
Consider the initial value problem dx -2x+y dt x(0) m, y(0) = = n. dy = -y dt 1. Draw a direction field for the system. 2. Determine the type of the equilibrium point at the origin 3. Use dsolve to solve the IVP in terms of mand n 4. Find all straight-line solutions 5. Plot the straight-line solutions together with the solutions with initial conditions (m, n) = (2, 1), (1,-2), 2,2), (-2,0)
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
2. Consider the linear system: - (1 2) Y.with initial conditions) Y dt a) Compute the...
2. Consider the linear system: - (1 2) Y.with initial conditions) Y dt a) Compute the eigenvalues and eigenvectors for the system. b) For each eigenvalue, pick an associated eigenvector V and determine a vector solution y(t) to the system. c) Draw an accurate phase portrait for this system. What type of equilibrium point is the origin?
Differential Equations Need Help! Will Rate! Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt...
Differential Equations Need Help! Will Rate!
Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt2. (15) 2. Verify that the two solutions are linearly independent. (5) 3. Build the general solution to the DE as a linear combination of these two solutions. (5) 4. Using the general solution, calculate the solution for the same DE with the initial conditions z(0) 5, x(0) 3. (10) Question...
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)
Consider the linear system. dy da dt = + 2y, at 9x + 4y. (1). Find...
Consider the linear system. dy da dt = + 2y, at 9x + 4y. (1). Find the eigenvalues. (2). Find the eigenvectors. (3). Determine the type and stability of the critical point(0,0). (4). Roughly sketch the phase portrait, including directions.
dy -X dx2 dt =2y-x dt 2. Consider the following system of equations: phase plane, showing...
dy -X dx2 dt =2y-x dt 2. Consider the following system of equations: phase plane, showing only the first quadrant. (a) Graph the nullclines on a (b) Find the fixed points (there are two) to determine the nature of each fixed point (i.e., source, sink, saddle, and (c) Use Jacobian analysis whether it is a node or spiral). (d) Draw the flow arrows in each region of your phase plane from part (a). You may use a computer to help...
1. Find the general solution to dr dt = x + 3y dy dt = 4.0...
1. Find the general solution to dr dt = x + 3y dy dt = 4.0 + 2y
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
Please solve this in Matlab
Consider the initial value problem dx -2x+y dt x(0) m, y(0) = = n. dy = -y dt 1. Draw a direction field for the system. 2. Determine the type of the equilibrium point at the origin 3. Use dsolve to solve the IVP in terms of mand n 4. Find all straight-line solutions 5. Plot the straight-line solutions together with the solutions with initial conditions (m, n) = (2, 1), (1,-2), 2,2), (-2,0)
2. Consider the linear system: - (1 2) Y.with initial conditions) Y dt a) Compute the eigenvalues and eigenvectors for the system. b) For each eigenvalue, pick an associated eigenvector V and determine a vector solution y(t) to the system. c) Draw an accurate phase portrait for this system. What type of equilibrium point is the origin?
Differential Equations Need Help! Will Rate!
Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt2. (15) 2. Verify that the two solutions are linearly independent. (5) 3. Build the general solution to the DE as a linear combination of these two solutions. (5) 4. Using the general solution, calculate the solution for the same DE with the initial conditions z(0) 5, x(0) 3. (10) Question...
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)
Consider the linear system. dy da dt = + 2y, at 9x + 4y. (1). Find the eigenvalues. (2). Find the eigenvectors. (3). Determine the type and stability of the critical point(0,0). (4). Roughly sketch the phase portrait, including directions.
dy -X dx2 dt =2y-x dt 2. Consider the following system of equations: phase plane, showing only the first quadrant. (a) Graph the nullclines on a (b) Find the fixed points (there are two) to determine the nature of each fixed point (i.e., source, sink, saddle, and (c) Use Jacobian analysis whether it is a node or spiral). (d) Draw the flow arrows in each region of your phase plane from part (a). You may use a computer to help...
1. Find the general solution to dr dt = x + 3y dy dt = 4.0 + 2y
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