Question: Differential equation boundary values

Dear Maple users

This might have been asked before, I'm asking because I believe the solution to my problem is simpler than what i found on google.

I have this problem:


Its Poisson equation in cylindrical coordinates (no z dependence). I can solve it as

Now, what I wonder is how to solve it wrt. boundary values.

I should be obtaining something as

How can I do this?

Thanks for help. 
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