If F is the vector field outside of the origin defined by
F(x,y)=[(ax+by)/(x^2+y^2),(cx+dy)/(x^2+y^2)]
Where
D={(x,y) : y>0}
Question: for which values of a,b,c & d is F conservative on the range D
A vector field, v= f(x,y)i+ g(x,y)j is "conservative" if and only if $\displaystyle \frac{\partial f}{\partial x}= \frac{\partial g}{\partial y}$ and $\displaystyle \frac{\partial f}{\partial y}= -\frac{\partial g}{\partial x}$.