What does the differential equation answer mean?

NODARman
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Homework Statement
-4(dx+dy)
Relevant Equations
What does -4(dx+dy) mean?
Hi, last semester I "solved" a full differential equation and the answer was (see the picture). What does it mean? Can I make a graphic with it or what? I really don't get it.

*Arrows are just a continuation of the main formula*

293482098_2905522343085816_5653388484348363792_n.jpg
 
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I don't see a differential equation
( something of the form ##f ' = g(x,y)## )
so I have no idea what you are doing.
Can you try to explain what you think you are doing?

## \ ##
 
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It looks like you are calculating the differential of f(x,y) = x^2/y at the point (x,y) = (-2,1).
 
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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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