there's actually a faster way to do this, it's applicable on superior ODEs that involves matrices and other stuff.
haven't you ever covered?
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.