xstart=-20; 
%xmax=9;  %% It works
xmax=11;  %% It does not work. The solution explodes.
A=chebop([xstart,xmax]);
x=chebfun('x',[xstart,xmax]);
A.op= @(x,y) diff(y,2)-x*y;
% N[AiryAi[-20],30]  -0.176406127077984689590192292219
% N[D[AiryAi[x], x] /. x -> -20, 30]  0.892862856736471238398409934114
A.lbc= @(y) [y-(-0.176406127077984689590192292219); diff(y,1)-0.892862856736471238398409934114];
S = A\0;
xlim auto; plot(S,'.-')