Differential equations- simultaneous equations

Jenkz
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Homework Statement



http://img228.imageshack.us/i/cimg5162f.jpg/

This isn't the usual format, so I hope it's still ok. It's just easier than writing it out on here. I can't work out how to form a simultaneous equation from (1) and (2).

When solved it should form the du/dx and dv/dx answers written.

The Attempt at a Solution



I have tried to work backwards from the answers, but I still can't figure it out. I've also tried re-arranging (1) to find du/dx or dv/dx and subbing into (2) and trying to re-arrange, but I can't get the answers either.

Help please?
 
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Nevermind, I've got it now. Just a stupid mistake.
 
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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