Question

Find phase portraits for the systems in Problems 38, 39 and 40.

Short answer

The phase portraits of the systems are $X\text{'}=\left(\begin{array}{cc}4& 5\\ -2& 6\end{array}\right)X,X\text{'}=\left(\begin{array}{cc}4& -5\\ 5& -4\end{array}\right)XandX\text{'}=\left(\begin{array}{cc}1& -8\\ 1& -3\end{array}\right)X$

Step-by-step solution

Determine the phase portrait

• A phase portrait is a geometric depiction of a dynamic system's trajectory in a phase plane.
• A distinct curve or point represents each set of beginning circumstances.
• In the study of dynamical systems, phase pictures are a useful tool.

Determine the phase portrait of the system

Phase portrait of the system

$X\text{'}=\left(\begin{array}{cc}4& 5\\ -2& 6\end{array}\right)X$is shown below.

Phase portrait of the system

$X\text{'}=\left(\begin{array}{cc}4& -5\\ 5& -4\end{array}\right)X$is shown below.

Phase portrait of the system

$X\text{'}=\left(\begin{array}{cc}1& -8\\ 1& -3\end{array}\right)X$ is shown below.

The phase portraits of the systems are$X\text{'}=\left(\begin{array}{cc}4& 5\\ -2& 6\end{array}\right)X,X\text{'}=\left(\begin{array}{cc}4& -5\\ 5& -4\end{array}\right)XandX\text{'}=\left(\begin{array}{cc}1& -8\\ 1& -3\end{array}\right)X$