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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.

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?