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Identity (x-y)^2

If y=[x+√(x²-...

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If y=[x+√(x²-1)]^m then prove that (1-x²)d²y/dx²-xdy/dx+m²y=0

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y = \sqrt{x + 1} - \sqrt{x - 1}

(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} - \frac{1}{4} y = 0

y = {sin}^{- 1} x

, then prove that

(1 - x^{2}) \frac{d^{2} y}{d x^{2}} - x \frac{d y}{d x} = 0

x^{m} y^{n} = (x + y)^{m + n}

\frac{d^{2} y}{d x^{2}} = 0

y = x e^{- x}

then prove that

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

y = e^{m . {cos}^{- 1} x}

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

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