what is the phase portrait of this system.

Question

what is the phase portrait of this system.

$$\begin{cases} \dot x_1&=-x_1+x_2\\ \dot x_2&=-x_2 \end{cases}$$

My work

I have solved this, and I got the general solution as, $$e^{\frac{x_1}{x_2}}=\frac c{x_2^2}$$

But I dont know how to sketch the phase portrait.

In some method i have the solution as, $$\begin{cases}x_1=c(1+t)e^t\\ x_2=0\end{cases}$$ Here also i couldnt draw the phase portrait. Am I correct in my approach? What i have to keep in mind in solving such problems? And how I can confirm the directions of the curves?

Answer 1

Typing streamplot -x+y,-y in the dialog box of WA yields this: