If y - sin-1 x2 Then- 1 - x2d2 ydx2 - x -dydx -

y(sin^ 1x)^2 dydx=2sin^1x√(1 x^2) √(1 x^2)dydx=2sin^ 1x √(1 x^2)d^2ydx^2+( x√(1 x^2))dydx=2√(1 x^2) (1 x^2)d^2ydx^2 xdydx=2 . ...

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Formation of a Differential Equation from a General Solution

If y = sin-...

Question

If $y = ({sin}^{- 1} x)^{2}$ Then, $(1 - x^{2}) d^{2} \frac{y}{d x^{2}} - x \cdot \frac{d y}{d x} =$

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Solution

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y = (s i n^{- 1} x)^{2} + (c o s^{- 1} x)^{2}, t h e n (1 - x^{2}) \frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} =

y = (s i n^{- 1} x)^{2} + (c o s^{- 1} x)^{2}

(1 - x^{2}) \frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} =

y = ({sin}^{- 1} x)^{2}

(1 - x^{2}) \frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} = 2

y = ({sin}^{- 1} x)^{2}

(1 - x^{2}) \frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} = 2

y = {({sin}^{- 1} x)}^{2} + c,

(1 - x^{2}) \frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} = 2

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