Q6--T0201

[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.

Also, please correct your post, instead of lambda1=-3 write \lambda_1=-3 and surround by dollar signs

Code: [Select]

$\lambda_1=-3$
What s/w did you use for a plot?