Differential equation substituition of new terms

delsoo
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Homework Statement




for this question, i sub u=xy and try to eliminate y in my working.. but how should i proceed since the term ux cannot be separated

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The Attempt at a Solution

 

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I do not understand what you did. Your u-s and y-s look the same. Eliminate y by replacing it with u/x. Note that xdy/dx+y=du/dx, and xy2=u2/x.

ehild
 

Thread 'Finding the nth roots of a complex number'

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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