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)