unstable equilibrium toward which all nearby solutions curves tend as t -> infinity means the same as all nearby solutions curves tend to an unestable equilibrium as t -> infinity
I was given a question; "Sketch a picture of a phase portrait that has an unstable equilibrium toward which all nearby solutions curves tend as t -> infinity"
How would this be possible since the definition of an unstable equilibrium is all the solution curves near an unstable equilibrium tends towards infinity as t->infinity.
Unless there was a typo and the question meant "asymptotically stable equilibrium"
I'm not sure what you are trying to tell me :\ Sorry.
I get that the question wants me to sketch a phase portrait that has an unstable equilibrium which all nearby solutions tend to. But, unstable equilibriums shoot solution curves off to infinity, so how can they tend towards it?