Miscellaneous Exercise Q6 Differential Equations - NCERT Maths Class 12

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Question

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

Text Solution

\begin{align}&\frac{{dy}}{{dx}} + \sqrt {\frac{{1 - {y^2}}}{{1 - {x^2}}}} = 0\\ &\Rightarrow \; \frac{{dy}}{{dx}} = - \frac{{\sqrt {1 - {y^2}} }}{{\sqrt {1 - {x^2}} }}\\& \Rightarrow \; \frac{{dy}}{{\sqrt {1 - {y^2}} }} = - \frac{{dx}}{{\sqrt {1 - {x^2}} }}\end{align}

Integrating both sides, we get:

\begin{align}& \Rightarrow \; {\sin ^{ - 1}}y = - {\sin ^{ - 1}}x + C\\ &\Rightarrow \; {\sin ^{ - 1}}x + {\sin ^{ - 1}}y = C\end{align}

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