f[x_,y_,c_] = 2*x - y/x + y^2/2 + c
solplot = ContourPlot[Evaluate[Table[f[x,y,c],{c,-8,4,2}]],{x,-5,5}, {y,-5,5},Axes->True,PlotPoints->50]

vplot = VectorPlot[{1,((2*x^2 + y)/(x - x^2*y))},{x,-6,6},{y,-6,6},VectorScale->{0.04,0.04,None},Axes->True,PlotRange->{{-5,5},{-5,5}}]

Show[vplot,solplot]