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

$\displaystyle x^3y''' - 3x^2y'' +7xy' - 8y = x + exp(2x) for x > 0$

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

$\displaystyle y=c_1x^2 + c_2x^2ln(x)+c_3x^2ln(x)^2$

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.