I read this topic and it is still confusing since the differential equation is a bit different:

I use only variable of t. That topic use dx/dt and dy/dt, thus I can’t really use it to my problem at hand.

This is the problem, and the solution. What I want to achieve is how to plot the spiral curve along with the arrow? Given the input of matrix A and the initial value x(0).

Something is weird with this example. At x0 the derivative is [-2,1] but the spiral curve clearly shows something like [0,1]. I haven’t looked carefully but perhaps this is just a poor drawing?

thus the coordinate is (1,0) at the beginning and x-axis is the x_{1} and y-axis is the x_{2} that is why the arrow is pointing to that way. the term e^{-2t} wil goes to 0 as t goes to infinity… that is why it is spiraling to (0,0).

That is from my understanding. Correct me if I am wrong… I know there are lots of silent reader who is an expert / more than PhDs here…

The problem is I want to draw the solution curve…

Can anyone help? Or just pray I can make it alone…
either way thanks folks! or aliens or vampires here…

The real solution is different from the cartoon. If you want something more like the cartoon try changing the exponential to be a smaller power… exp(-t/2) for example