# Toronto Math Forum

## MAT244-2018S => MAT244--Tests => Quiz-6 => Topic started by: Victor Ivrii on March 16, 2018, 08:09:14 PM

Title: Q6--T0201
Post 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 real-valued functions.
b. Also draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as $t\to \infty$.
$$\mathbf{x}' =\begin{pmatrix} -2 &1\\ 1 &-2 \end{pmatrix}\mathbf{x}$$
Title: Re: Q6--T0201
Post by: Ge Shi on March 17, 2018, 12:11:47 AM
(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.

Title: Re: Q6--T0201
Post by: Victor Ivrii on March 17, 2018, 05:02:28 AM
Do not use external images; they will disappear at some moment. Please attach to your post.

$\lambda_1=-3$