I've been working on this one for about 3 hours and can't seem to find a solution for it:

I understand it's a 3rd order Cauchy-Euler and I've solved for the characteristic solution as:

Now, I have no idea how to find the solution when g(x) = x + exp(2x). I've tried using the Variation of Parameters technique only to arrive at ugly integrals. I'm assuming you have to make some sort of substitution.

Any help, much appreciated. Thanks.