In[]:=
sol=First@NDSolve[{y'[x]==y[x]Cos[x+y[x]],y[0]==1},y,{x,0,200}]
Out[]=
yInterpolatingFunction
Domain: {{0.,200.}}
Output: scalar

In[]:=
Plot[y[x]/.sol,{x,0,200},PlotRange->All]
Out[]=
In[]:=
A=Transpose[{(y/.sol)["Coordinates"][[1]],(y/.sol)["ValuesOnGrid"]}];
In[]:=
ByteCount[A]
Out[]=
191592
In[]:=
A1=Compress[A];
In[]:=
ByteCount[A1]
Out[]=
43008
In[]:=
ByteCount[A]
ByteCount[A1]
//N(*4.5timeslessofbytes*)
Out[]=
4.4548
In[]:=
ListLinePlot[Uncompress[A1],PlotRange->All]
Out[]=