MAT244-2018S > Quiz-6

Q6--T0401

(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}

3 &-2\\

2 &-2

\end{pmatrix}\mathbf{x}$$

**Ge Shi**:

(a)

https://imgur.com/a/W9njS

(b)

When t approaches to infinity:

if C2 is not equal to zero ,the solution is unbounded.

if C2 is equal to zero, the solution approaches to zero.

Since $\lambda_1=-1$ , $\lambda_2=2$

Eigenvalues are real but unequal and have the opposite signs, x=0 is a saddle point and unstable.

I've attached the graph.

**Victor Ivrii**:

See my comment to your other post. And do not try to cover the same quiz in other sections!

**Ge Shi**:

(a)

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