3
$\begingroup$

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

  • 0
    @Chandrasekhar,question is about method for solving DE. Which method you suggest ?2011-11-12

1 Answers 1

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 $x=c\sqrt{1-y^2}-y\sqrt{1-c^2}.$

  • 0
    Thanks, after dividing with $\sqrt{(1-x^2)(1-y^2)}$ problem looks much simpler.2011-11-13