Find the equilibria points of the following system. dx/dt = (x-1)[r-1-(x-1)^2]. Here r is a real...
(5 points) Find all 5 equilibria for the system of first order ODES dx = x(4-y-12) dt dy = y(x2-1) dt
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
1 point) Solve the system 5 -1 dx lc dt 2 with x (0) = Give your solution in real form. An ellipse with clockwise orientation 1. Describe the trajectory.
1 point) Solve the system 5 -1 dx lc dt 2 with x (0) = Give your solution in real form. An ellipse with clockwise orientation 1. Describe the trajectory.
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to find the linear approximation at each of the critical points. Determine the type and the stability. . Briefly describe the overall behavior of r and y
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to...
(1 point) Solve the system 2 1 dx dt х -5 -2 N with x(0) = 3 Give your solution in real form. X= X2 = An ellipse with clockwise orientation ✓ 1. Describe the trajectory.
dx/dt= -2 -5 5 -2 x(0)= 2 4 Solve the system dx/dt = [-2 -5; 5 -2]x with x(0) = [2 4]. NOTE: *Give Solutions in real form x1=_____ and x2=________
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...
(1 point) Solve the system -3 -3 dx = х dt :: 1:) with x(0) = Give your solution in real form. Xi = X2 = An ellipse with counterclockwise orientation 1. Describe the trajectory.
(1 point) Solve the system 4 -2 dx II dt 10 -4 -3 with x(0) = -2 Give your solution in real form. Xı = -3cos(21)+(27sin(2t))/5 x2 = -2cos(2t)-11 sin(2t) An ellipse with counterclockwise orientation 1. Describe the trajectory.