A solution to a homogeneous system

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Homework Statement



I know there is a polynomial that is a solution to the equation:

3/2f(x) - x/2f'(x) - f''(x)=x



Homework Equations





The Attempt at a Solution


I tried many polynomials of degrees 1,2 and 3, but they do not work in my equation
 
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What happens when you back-substitute f(x)=x?
 
I think you want http://en.wikipedia.org/wiki/Method_of_variation_of_parameters" for this problem.
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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