If frac{dy}{dx} + frac{1}{sqrt{1 - x^2}} = 0, | vedclass

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(A) Given the differential equation: $\frac{dy}{dx} + \frac{1}{\sqrt{1 - x^2}} = 0$Rearranging the terms,we get: $\frac{dy}{dx} = -\frac{1}{\sqrt{1 -

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$y + \sin^{-1}x = c$

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(A) Given the differential equation: $\frac{dy}{dx} + \frac{1}{\sqrt{1 - x^2}} = 0$Rearranging the terms,we get: $\frac{dy}{dx} = -\frac{1}{\sqrt{1 - x^2}}$By separating the variables,we have: $dy = -\frac{1}{\sqrt{1 - x^2}} dx$Integrating both sides: $\int dy = -\int \frac{1}{\sqrt{1 - x^2}} dx$We know that $\int \frac{1}{\sqrt{1 - x^2}} dx = \sin^{-1}x + c$Therefore,$y = -\sin^{-1}x + c$Rearranging the terms gives: $y + \sin^{-1}x = c$

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

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