Solving H.S. Bear's Diff Eq Problem: (1-y^{2}) dx - xy dy = 0

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The forum discussion centers on solving the differential equation (1-y²) dx - xy dy = 0, as presented in H.S. Bear's book "Diff Eq: Concise Course." The solution to this equation is confirmed to be (x²)(1-y²) = c. The user initially struggled with the problem but resolved their confusion by correctly applying the separation of variables technique and addressing a sign error in their calculations.

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bryanosaurus
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I am reviewing differential equations, going through H.S. Bear's book Diff Eq: Concise Course.
The problem set for the variables separate section were pretty easy and straightforward except for this one, which I can't see how to arrive at the answer given in the book. I'm probably just missing something silly, so maybe another pair of eyes looking at it will clear it up.

(1-y^{2}) dx - xy dy = 0

the solution given is (x^{2})(1-y^{2}) = c
 
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Hi bryanosaurus! :smile:
bryanosaurus said:
(1-y^{2}) dx - xy dy = 0

erm … dx/x = ydy/(1 - y²) … ? :smile:
 
Okay I got it now, I was fudging a sign when getting rid of the natural logs.
Thanks :)
 

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