VectorPlot[{1/((1^2+x^2y^2/9)^(1/2)),x y /(3(1^2+x^2y^2/9))},{x,-3,3},{y,-3,3}]

VectorPlot[{1/((1+(y-x)^2)^(1/2)),(y-x)/((1+(y-x)^2)^(1/2))},{x,0,7},{y,-7,7}]

VectorPlot[{1,y (4-y) /12},{x,-3,7},{y,0,5}]