Solve perturbation problem with mathematica

[rodiena]

u'(1-epsilon(u')^2)=-y      perturbation problem

u0(1)=0   u1(1)=0          boundary conditions

u=u0+epsilon(u1)            direct opening
u'=(u0)'+epsilon(u1)' 

I need solve perturbation problem with mathematica program.Thanks...

Edited December 9, 2017 by rodiena