Question:
Find the general solution of the differential equation:
\(\frac {dy}{dx}+\sqrt {\frac {1-y^2}{1-x^2}}=0\)
Find the general solution of the differential equation:
\(\frac {dy}{dx}+\sqrt {\frac {1-y^2}{1-x^2}}=0\)
Updated On: Sep 19, 2023
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Solution and Explanation
\(\frac {dy}{dx}+\sqrt {\frac {1-y^2}{1-x^2}}=0\)
⇒\(\frac {dy}{dx}=-\sqrt {\frac {1-y^2}{1-x^2}}\)
⇒\(\frac {dy}{\sqrt {1-y^2}}=-\frac {dx}{\sqrt {1-x^2}}\)
Integrating both sides, we get:
\(sin^{-1}y=-sin^{-1}x+C\)
⇒\(sin^{-1}x+sin^{-1}y=C\)
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