Find the general solution of the following system and determine the type and stability of critical...
Please find general solution and find the type and stability of critical point (0,0) x ]' = [1 2 [x [y -5 -1] y ]
3. (2 points) Determine the stability and the type of the critical point(s) of the following system of differential equations 1-441-yi
7. Find and classify the type and stability of the critical point for each system below x' =-2x1-3x2 + 8 xz'= 3x1 + 2x2-8 Where α is a real number.
Problem 6: For the following system of 1st order ODEs, a) When k - 1, determine the type of the critical point at (20) and check if it is going to be stable. And find the solution for yi and y2 at the critical point 01-20) b) Find the k values required to ensure that the system at the critical point (1 2is spiral and stable
Problem 6: For the following system of 1st order ODEs, a) When k -...
Consider the nonlinear System of differential equations di dt dt (a) Determine all critical points of the system (b) For each critical point with nonnegative x value (20) i. Determine the linearised system and discuss whether it can be used to approximate the ii. For each critical point where the approximation is valid, determine the general solution of iii. Sketch by hand the phase portrait of each linearised system where the approximation behaviour of the non-linear system the linearised system...
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.
The following system can be interpreted as a competition system describing the interaction of two species with populations x(t) and y(t) x' 40x – 22 – ry y' = 30y - y2 – 0.5xy This system has four critical points (0,0), (0, 30), (40,0), and (20, 20). (a) At critical point (20, 20), find the linearization of the system and its eigenvalues. Deter- mine the type and stability of the critical point (20, 20). Base on your work in part...
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
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...
2 - 5 For each system below, (a) solve the initial value problem, and (b) determine the type and stability of the critical point at (0,0). x'= 5x - 5x2 X2' = 2xı + 3x2 xi(–117) = 7, x2(–117) = 3.