I am working on a project for my Differential Equations class and am stuck at the very last stage of the project. I have solved the problem up to the following equation:

y = 1/2 [ (1-x)^(1+b/a)/(1+b/a) - (1-x)^(1-b/a)/(1-b/a) ] + (a*b)/(a^2-b^2)

Now I need to find out what this equation becomes ifa=b. If I setaequal tobthe equation becomes:

y = 1/2 [ (1-x)^2/2 - 1/0] + a^2/0

Notice that there are two divisions by 0. This equation basically turns in to some term minus infinity plus infinity. It occurred to me that I can use La' Hopital's rule by rewriting the undefined portion of the equation in terms of the limit asaapproachesbto find what its value becomes. However, I'm struggling to actually solve this problem.

I already know what the answer is:

y = 1/2 { 1/2 [ (1-x)^2 - 1 ] - ln(1-x) }

I just don't know how to get this answer. Any help is solving this will be much appreciated.

P.S. Sadly, my teacher only gave my class a week to do this project, and tomorrow's the deadline. I need to try to get this done tonight if at all possible.