### Author Topic: Q6--T0201  (Read 2025 times)

#### Victor Ivrii

• Elder Member
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##### Q6--T0201
« 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 $t\to \infty$.
$$\mathbf{x}' =\begin{pmatrix} -2 &1\\ 1 &-2 \end{pmatrix}\mathbf{x}$$
« Last Edit: March 16, 2018, 08:10:48 PM by Victor Ivrii »

#### Ge Shi

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##### Re: Q6--T0201
« Reply #1 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.

« Last Edit: March 17, 2018, 12:48:14 PM by Ge Shi »

#### Victor Ivrii

$\lambda_1=-3$