-2 | -5 |
5 | -2 |
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=________
(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.
(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.
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.
(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 3 9 da dt 2 -1 -3 2 with x(0) 4 Give your solution in real form. 21 = 22 =
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)
9. Use the Laplace transform to solve the system dx -xty dt dy dt x(0) = 0, y(0) = 1 = 2x
6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x) = x/2-44 a. Find the equilibrium points. (5 pts.) b. Find the linearized system around each equilibrium point. (5 pts.) C. Which of these equilibrium points is (are) and what the pole values for the stable equilibrium points? (5 pts.) 6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x)...
use the Laplace transform to solve the given system of differential equations dx dt dx dt dt dt x(0) 0, y(o)0 x(t) =
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.