(Dulac’s test)For the system show that there are no closed paths in a simply connected region in which is of one sign, where ρ(x,y)is any function having continuous first partial derivatives. 1....

(Dulac’s test)For the system

show that there are no closed paths in a simply connected region in which

is of one sign, where ρ(x,y)is any function having continuous first partial derivatives.

1. show that curl(X)=0may be replaced by curl (ψX)=0, where ψ (x,y) is of one sign in D.