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x^2 (d^2y/dx^2) + 3x (dy/dx) - 3y = x

The boundary conditions:

y(x=1) = 0

y(x=2) = 1

It's been awhile since I took diffeq, but my research has led me to believe that this is not a Cauchy-Euler Equation since it is not equal to 0, it cannot be separated for separation of variables, it cannot be solved using reduction of order because I was not given one solution, and I cannot solve using Laplace transforms because I was not given initial values, just boundary conditions.

I considered dividing by x^2 or x, but that leaves me either with a constant (still not 0) or a term that has both x and y in it, which I wouldn't know how to solve either.

I just re-imaged my laptop so I do not currently have MATLAB, but if I did I would not be quite sure how to go about it. WolphramAlpha didn't read the equation correctly. I have flipped through a friend's diffeq book and that yielded nothing helpful.

It seems likely that this has a simple solution because this homework was intended as a review of diffeq, so I'm sure a large part of the problem is that I'm rusty and have overlooked something. Help?