Dirichlet and Robin boundary condition

*I have worked a lot on this problem but unfortunately more I work more get confused , a differential problem whit Dirichlet and Robin boundary condition. And the most difficult thing which I think is the only problem for me is the right boundary condition, while I don't know if I do completely wrong..

How can I solve this differential equation using MATLAB?*

[Sepehr]

Nobody knows ?!!

[Christian Chamberlayne]

you can use a shooting method.

use ODE 45 with u(0) = 0 and loop through a set of guesses for u'(0)

Then evaluate your guesses for how close they are to satifying u'(1) + u(1) = 5

converge on the correct guess for u'(0) that meets u'(1) + u(1) = 5