The discussion revolves around demonstrating that the origin is the only critical point for a system of differential equations defined by the equations x' = -x - x^3 and y' = -y - y^5. The original poster expresses uncertainty due to missed lectures and seeks assistance in understanding the problem.
The conversation is ongoing, with participants questioning the correctness of the equations and exploring the implications of the identified critical points. There is no explicit consensus, but guidance on the differentiation process has been provided.
There is a noted concern regarding a possible typo in the second equation, which may affect the interpretation of the problem. The original poster's missed lectures due to a medical issue adds context to their request for help.
Kamekui said:Homework Equations
x'= -x-x3
y-= -y-y5
Kamekui said:Homework Statement
Show the origin is the only critical point
Homework Equations
x'= -x-x3
y-= -y-y5
The Attempt at a Solution
I'm not really sure how to go about this. I missed a few lectures due to a medical issue, and now were at the end of the semester and I can't get in touch with the professor. Any help would be appreciated.
sharks said:Your second equation doesn't make sense. The very first step when asking for help, is to always make sure that you have typed your question correctly. There is a minus after y. Is there supposed to be another constant or variable after the minus sign? Or is that minus sign not supposed to be there?
Anyway, to find the critical point, you should differentiate the function with respect to the independent variable and then equate to 0.
LCKurtz said:It doesn't take much imagination to figure out that the second equation is ##y'=-y-y^5##. This is a system of two differential equations. The stationary points are where ##x'## and ##y'## are simultaneously zero.