# Thread: Critical points and phase portraits

1. ## Critical points and phase portraits

Find the critical points and phase portrait of the given autonomous first-order differential equation: dx/dt=x^2 - x^4. Classify each critical point as asymptotically stable, semi-stable, or unstable. Sketch the graph of a typical solution x(t) where x0 has the given values: (a) x0>1 (b) 0<x0<1 (c) -1<x0<0 (d) x0<-1.

2. What did you get for $x(t)$ ?

3. I got (x∙ln(|x+1|)-x∙ln(|x-1|) - 2)/2x but couldn't figure out how to solve for x.

4. Originally Posted by kiddopop
I got (x∙ln(|x+1|)-x∙ln(|x-1|) - 2)/2x
what is this equal to?

5. (x∙ln(|x+1|)-x∙ln(|x-1|) - 2)/2x = t

6. I understand. I was going about the problem in the completely wrong way.