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$If x^{2} (x^{2} - 1) \frac{d y}{d x} + x (x^{2} + 1) y = x^{2} - 1 then y (x - \frac{1}{x}) - \ln x =$

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c+12x2

c−12x2

c+1x2

c−1x2

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Correct option is A

dydx+x2+1xx2−1y=1x2 I. F=exp⁡∫x2+1dxx(x−1)(x+1)=x2−1x Sol. Is yx2−1x=∫x2−1x3dx=ln⁡x+12x2+c⇒yx−1x−ln⁡x=C+12x2

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If x2x2−1dydx+xx2+1y=x2−1 then yx−1x−ln⁡x=

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$If x^{2} (x^{2} - 1) \frac{d y}{d x} + x (x^{2} + 1) y = x^{2} - 1 then y (x - \frac{1}{x}) - \ln x =$