a) Proof:
Consider the system ## \dot{x}=x+x^3-y^2 ## and ## \dot{y}=x^2-x^4+y^5 ##.
By theorem, Bendixson's negative criterion states that there are no closed paths in a simply connected region of the phase plane on which ## \frac{\partial X}{\partial x}+\frac{\partial Y}{\partial y} ## is of...