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Differential equation with general solution ${y = (\sin^{- 1} x)}^{2} + A (\cos^{- 1} x) + B$ where A , B are arbitrary constants is ____. $(y_{1}, y_{2} d e r i v a t i v e s o f y)$

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$(1 + x^{2}) y_{2} - x y_{1} = 2$

$(1 - x^{2}) y_{2} - x y_{1} = 1$

$(1 - x^{2}) y_{2} - x y_{1} = 2$

$(1 - x^{2}) y_{2} + x y_{1} = 2$

answer is C.

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Detailed Solution

$\begin{array}{l} y_{1} = \frac{2 \sin^{- 1} x}{\sqrt{1 - x^{2}}} - \frac{A}{\sqrt{1 - x^{2}}} \\ \Rightarrow \sqrt{1 - x^{2}} . y_{1} = 2 \sin^{- 1} x - A \end{array}$

Again differentiate

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