h[x_,y_]=x Cos[y]+y^2

cplot=ContourPlot[h[x,y],{x,-10Pi,10Pi},{y,-5Pi,5Pi},
ContourShading->False,
Contours->{h[-7Pi,7Pi/2],h[-3Pi,3Pi/2],h[Pi,Pi/2],h[5Pi,5Pi/2],h[9Pi,9Pi/2]},
PlotPoints->50]

eqpts=Graphics[{Red,AbsolutePointSize[4],Table[Point[{(-1)^n(2n+1)Pi,(2n+1)Pi/2}],{n,-5,5}]}]

allplot=Show[cplot,eqpts,FrameTicks->{Table[n Pi,{n,-10,10,2}],Table[n Pi/2,{n,-9,10,2}],None,None}]

Export["Problem5_3_3.png",allplot]