Level Sets of L

[nimble flume]

Hi! I have proven that the given function is a Lyapunov function but I'm confused on how to sketch the level sets of L. Any help is appreciated! :)

[smoky bramble]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[ionic wagon]

Just use Desmos to get an idea of the graphs

[nimble flume]

Is there a way to sketch it without using Desmos?

[ionic wagon]

Yeah, you get y^2=cubic in x, so y=+-sqrt(cubic)

So sketch the cubic, then argue what the radical does

[nimble flume]

I’m sorry; I don’t understand. Do I do the x-null and y-null?

[ionic wagon]

what's an x-null

[nimble flume]

Nullclines

Where dx/dt = 0 and dy/dt = 0