MAT244-2018S > Quiz-6

Q6--T0201

(1/1)

Victor Ivrii:
a. Express the general solution of the given system of equations in terms of real-valued functions.
b. Also draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as $t\to \infty$.
$$\mathbf{x}' =\begin{pmatrix} -2 &1\\ 1 &-2 \end{pmatrix}\mathbf{x}$$

Ge Shi:
(a)
In the attachement

(b)
When t approaches to infinity, the solution is approaches to zero

Since $\lambda_1=-3$ , $\lambda_2=-1$
Eigenvalues are real but unequal and have the same sign, x=0 is a node and asymptotically stable.

Victor Ivrii:
Do not use external images; they will disappear at some moment. Please attach to your post.

--- Code: ---$\lambda_1=-3$