Solving for u: Struggling with a 2D Homework Problem

dirk_mec1
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Homework Statement



1.PNG

The Attempt at a Solution



I don't know how to choose u. I presume we look in 2D; I thought u should look something like:

u = \left[ \begin{array}{c} \psi \\ \psi \end{array} \right]

and c= \phi but that isn't correct.
 
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How about picking two vector fields? Pick u=(psi,0) for the first part and u=(0,psi) for the second part.
 
Dick said:
How about picking two vector fields? Pick u=(psi,0) for the first part and u=(0,psi) for the second part.

Yes of course, thanks Dick!
 
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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