Question

Find the general solution of the differential equation:
\(\frac {dy}{dx}+\sqrt {\frac {1-y^2}{1-x^2}}=0\)

Answer 1

\(\frac {dy}{dx}+\sqrt {\frac {1-y^2}{1-x^2}}=0\)

⇒\(\frac {dy}{dx}=-\sqrt {\frac {1-y^2}{1-x^2}}\)

⇒\(\frac {dy}{\sqrt {1-y^2}}=-\frac {dx}{\sqrt {1-x^2}}\)

Integrating both sides, we get:

\(sin^{-1}y=-sin^{-1}x+C\)

⇒\(sin^{-1}x+sin^{-1}y=C\)