Question

Solve the following system of equations

dx/dt = -4x -2y
dy/dt =5x+2y
(a.) Find the equilibrium point.
(b.) Write the system in matrix form X' = AX.

Answer 1

The equilibrium point is (0,0). The system can be written in matrix form X' = AX, where X is a column matrix and A is a 2x2 matrix.

Step-by-step explanation:

To find the equilibrium point, we need to solve the system of equations:

dx/dt = -4x - 2y

dy/dt = 5x + 2y

(a) Equilibrium point occurs when both derivatives are zero:

-4x - 2y = 0

5x + 2y = 0

Solving these equations, we get x = 0 and y = 0. So the equilibrium point is (0,0).

(b) To write the system in matrix form, we have:

X' = AX

Where X is the column matrix [x, y] and A is the matrix [[-4, -2], [5, 2]].