Linearity of boundary conditions

sarideli18
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Homework Statement



Using the definition of linearity to determine whether or not ech case is a linear homegeneous boundary condition:

i.) Uxx(0,y)=Ux(0,y)U(0,y)
ii.)Uy(x,0)=Ux(5,y)

Homework Equations





The Attempt at a Solution



I know Uxx(0,y)=Ux(0,y)U(0,y) is not linear because of U(0,y). However, I have no idea for ii.
 
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Well, what does "linear" mean?
 
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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