Toronto Math Forum
MAT2442018S => MAT244Tests => Quiz6 => Topic started by: Victor Ivrii on March 16, 2018, 08:09:14 PM

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

(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.

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