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Which method should I use for solving equation $\sqrt{1-x^2}dy + \sqrt{1-y^2}dx = 0$ ?

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separable equations... – pedja Nov 12 '11 at 16:03
integrals of irrational functions – pedja Nov 12 '11 at 16:08
@pedja: I don't think he is asking that. I think he is interested in knowing if $\sin^{-1}(x) = \cos^{-1}(y)$, then how does one solve for $y$. – user9413 Nov 12 '11 at 16:11
Ah never mind, for some reason I had $dy$ and $dx$ switched. Yes, just use separation of variables. – user7530 Nov 12 '11 at 16:21
@Chandrasekhar,question is about method for solving DE. Which method you suggest ? – pedja Nov 12 '11 at 16:26

1 Answer

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Use the perfect hints by pedja and user7530. So dividing both sides by $\sqrt{(1-x^2)(1-y^2)}$ you will be left with something like $$d(\sin^{-1}x+\sin^{-1}y)=0.$$ You may also wish to write the general solution as $$x\sqrt{1-y^2}+y\sqrt{1-x^2}=c$$ or $$x=c\sqrt{1-y^2}-y\sqrt{1-c^2}.$$

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Thanks, after dividing with $\sqrt{(1-x^2)(1-y^2)}$ problem looks much simpler. – 1osmi Nov 13 '11 at 10:51

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