The discussion revolves around classifying the fixed points of a given linear system and determining their stability. The system is defined by the equations \(\dot{x}=x + y\) and \(\dot{y}=x + 3y\), with a focus on the fixed point at (0,0).
The discussion is ongoing, with participants seeking clarification on the concept of stability and the methods to test it. Some guidance has been offered regarding the use of eigenvalues, but no consensus has been reached on the classification of the fixed point.
There appears to be confusion regarding the interpretation of the fixed point and the mathematical implications of the expression dy/dx = 0/0. Participants are also navigating the constraints of their homework requirements.
0/0 is not a number, so how can you say that there is a fixed point at dy/dx = 0/0?coverband said:Homework Statement
Classify the fixed points of the following linear system and state whether they are stable or unstable
\dot{x}=x + y
\dot{y} = x + 3y
Homework Equations
The Attempt at a Solution
Fixed point at dy/dx = 0/0. Therefore fixed point = (0,0)
How does one test for stability?
Thanks
coverband said:How does one test for stability?