Question

Solve:

$x\sqrt{1-y^2}dx+y\sqrt{1-x^2}dy=0$

Answer 1

Given the differential equation,

$x\sqrt{1-y^2}dx+y\sqrt{1-x^2}dy=0$

or, $\frac{x}{\sqrt{1-x^2}}dx+\frac{y}{\sqrt{1-y^2}}dy=0$

Now integrating both sides we get,

$\sqrt{1-x^2}+\sqrt{1-y^2}=c$. [ Where $c$ is integrating constant]