# Phase Portrait Question

1. Apr 29, 2004

### MathematicalPhysics

Hello, I'm considering the system:

dx/dt=y-x

dy/dt=x-y

I've found the fixed points and shown that this is a first integral of the system:

f(x,y)=x+y

How can I (using this information only) sketch a phase portrait? I know the graph of fixed points looks like the x=y graph, but im not sure how this relates to a phase portrait.

Any help? Thanks.

2. Apr 29, 2004

### arildno

From my slight acquaintance with phase portraits( among lots of other stuff..), I'd say the
equations f(x,y)=x+y=const. for different constants defines your phase portrait.
In particular, it would be important to graph whether solutions converge towards some fixed point at x=y (i.e stable fixed points), or if the fixed points are unstable/saddle-like.