f[x_,y_]:=2*x+Sin[y];
g[x_,y_]:=x*Cos[y];
V[x_,y_]:=-x^2-Sin[y]*x;

plot1=StreamPlot[{f[x,y],g[x,y]},{x,-π,π},{y,-2*π,2*π},StreamPoints->60,StreamStyle->Black];
plot2=ContourPlot[f[x,y]==0,{x,-π,π},{y,-2*π,2*π},ContourStyle->{Thick,Red}];
plot3=ContourPlot[g[x,y]==0,{x,-π,π},{y,-2*π,2*π},ContourStyle->{Thick,Green},PlotPoints->100];
plot4=ContourPlot[V[x,y],{x,-π,π},{y,-2*π,2*π},AspectRatio->Automatic];
Show[plot4,plot1,plot2,plot3]