h[t_,x_,y_]={x, y+t(Sin[x]-Exp[x])}
Manipulate[Dots=ListPlot[Table[Table[h[t,i/4,j/4],{i,-20,20}],{j,-20,20}],PlotRange->{{-5,5},{-2,5}}];
Graph=Plot[h[t,x,Exp[x]][[2]],{x,-5,5}];
Show[{Dots,Graph}],{t,0,1}]