Existence uniqueness wronskian

bl4ke360
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Homework Statement



y''-4y=12x

Homework Equations



I don't know

The Attempt at a Solution



http://imageshack.us/a/img7/944/20130207102820.jpg

I'm not sure if I did this right, I'm putting this here to make sure. Please respond within 3 hours if you can because it will be due.
 
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bl4ke360 said:

Homework Equations



I don't know

Really? I would have thought this "Theorem 3.1.1" would be relevant.

The rest of the answers seem fine.
 


Karnage1993 said:
Really? I would have thought this "Theorem 3.1.1" would be relevant.

The rest of the answers seem fine.

Well theorem 3.1.1 is a paragraph long, and not really an equation either. I'm not sure about letting c=-3 though, the only reason I did is because wolfram had it as part of the answer but I don't see how.
 
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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