Which method should I use for solving equation $\sqrt{1-x^2}dy + \sqrt{1-y^2}dx = 0$ ?
Nonlinear differential equation type
3
$\begingroup$
ordinary-differential-equations
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0separable equations... – 2011-11-12
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0[integrals of irrational functions](http://en.wikipedia.org/wiki/List_of_integrals_of_irrational_functions) – 2011-11-12
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0@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 $y$. – 2011-11-12
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0Ah never mind, for some reason I had $dy$ and $dx$ switched. Yes, just use separation of variables. – 2011-11-12
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0@Chandrasekhar,question is about method for solving DE. Which method you suggest ? – 2011-11-12
1 Answers
3
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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0Thanks, after dividing with $\sqrt{(1-x^2)(1-y^2)}$ problem looks much simpler. – 2011-11-13