Which method should I use for solving equation $\sqrt{1-x^2}dy + \sqrt{1-y^2}dx = 0$ ?
Nonlinear differential equation type
3
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ordinary-differential-equations
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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