F= DSolve[{y'[x] == (x*y[x]-y[x]*y[x])/x^2,y[1]==2},y,x]//Quiet

TruePlot = Plot[Evaluate[y[x]/.F],{x,1,3}, PlotStyle->{Red,Thickness[0.001]}];

This was with h=0.01, points = 201

ODEData3 = Import["C:\\Users\\kfrin\\Desktop\\MPI\\ODEsoln3.dat"];

APDataPlot3 = ListPlot[ODEData3, PlotStyle->Blue];

Show[TruePlot, APDataPlot3]

ODES[x_]:=Evaluate[y[x]/.F][[1]]

ODES[1]

DiffData = Table[{ODEData3[[i,1]],Abs[ODES[ODEData3[[i,1]]]-ODEData3[[i,2]]]},{i,1,Length[ODEData3]}];

ListPlot[DiffData]

This was with h=0.001, points = 2001

ODEData4 = Import["C:\\Users\\kfrin\\Desktop\\MPI\\ODEsoln4.dat"];

APDataPlot4 = ListPlot[ODEData3, PlotStyle->Cyan];

Show[TruePlot, APDataPlot3, APDataPlot4]

DiffData2= Table[{ODEData4[[i,1]],Abs[ODES[ODEData4[[i,1]]]-ODEData4[[i,2]]]},{i,1,Length[ODEData4]}];

ListPlot[{DiffData,DiffData2}, PlotStyle->{{Red, PointSize[Large]},{Blue,PointSize[Small]}}]