(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all the points [itex] p \in \mathbb R^2 [/itex] such that [itex] df_p =0 [/itex] where

[tex] df = \frac{ (y^2-x^2) dx - 2xy dy }{(x^2+y^2)^2} [/tex]

3. The attempt at a solution

I figure the way this should be done is by solving the differential equation derived from

[tex] (y^2-x^2) dx - 2xy dy =0 .[/tex]

It's either that or just find when the coefficients are identically zero. I can do either quite easily once I know for sure which I should be doing. Thoughts?

Edit: My only issue is that if I solve the differential equation, I will technically have a constant that I can't get rid of. Is there a canonical way of setting such a constant? Or is the solution the whole one-parameter family dictated by possible choices of the constant?

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# Homework Help: Finding when covector disappears

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