(************************************************)
(* Singular perturbation: ϵ y'' - (x^2) y' - y = 0;
   y(0) = 1;  y(1) = 1                        *)
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Remove["Global`*"]
(* Outer solution *)
DSolve[(x^2) p'[x]+p[x]==0,p[x],x]

Remove["Global`*"]
(* Inner solution *)
DSolve[{q''[X]-q'[X]==0,q[0]==1},q[X],X]

Remove["Global`*"]
(* Exact solution *)
ϵ=0.05;
s=NDSolve[{ϵ y''[x]-(x^2) y'[x]-y[x]==0,y[0]==1,y[1]==1},y[x],x];
ypert= (E^((x-1)/ϵ))+(E^(-x/(ϵ^(1/2))));

Plot[{Evaluate[y[x]/.s],ypert},{x,0,1},PlotStyle->Thick]