MAT244-2018S > Quiz-6

Q6--T0201

(1/1)

**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: ---$\lambda_1=-3$

--- End code ---

What s/w did you use for a plot?

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