General Solutions for Trivial High Order PDEs

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I should find the general solution of the two following trivial PDEs.

<br /> u=u(x_1,x_2,...,x_n)<br />

1)

<br /> \frac{\partial u}{\partial x_1 \partial x_2} = 0<br />

2)

<br /> \frac{\partial u}{\partial x_1} - u = 0<br />
 
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What in particular are you having trouble with?
 
What have you tried? Per forum rules, you need to show some effort at solving the problem.
 
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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