Plot[{x^2-2*x+.5,x^2-2*x+.25,x^2-2*x+.01},{x,-3,4},PlotStyle->Thick,TicksStyle->Large,AxesLabel->{"x","y"},PlotRange->{-1,10},PlotLegends->Placed[{"","",""},Right]]

plot1=Plot[{.1*x^3-x+1,.01*x^3-x+1,.005*x^3-x+1},{x,-20,20},PlotStyle->Thick,TicksStyle->Large,AxesLabel->{"x","y"},PlotLegends->Placed[{"","",""},Right],PlotRange->{-20,20}];plot2=Plot[-x+1,{x,-20,20},PlotStyle->{Dashed,Red}];
Show[plot1,plot2]

f[x_]:=NIntegrate[Exp[-y^2],{y,x,∞}];
Plot[{f[x],Exp[-x^2]/(2*x),Exp[-x^2]/(2*x)*(1-1/(2*x^2)),Exp[-x^2]/(2*x)*(1-1/(2*x^2)+3/(4x^4))},{x,1,2},PlotStyle->Thick,TicksStyle->Large,AxesLabel->{"x","y"},PlotLegends->Placed[{"","","",""},Right]]

ϵ=.2;
s=NDSolve[{x''[t]==-1/(ϵ*x[t]+1)^2,x[0]==0,x'[0]==1},x,{t,0,2.3}]
Plot[{Evaluate[x[t]/.s],-1/2*t^2+t,-1/2*t^2+t+ϵ*(-t^4/12+t^3/3)},{t,0,2.3},PlotRange->{0,.6},PlotStyle->Thick,TicksStyle->Large,AxesLabel->{"τ","X"},PlotLegends->Placed[{"","",""},Right]]