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Question

If xy2=1, prove that 2dydx+y3=0

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Solution

We have, xy2=1 ...i
Differentiating with respect to x, we get,

ddxxy2=ddx1xddxy2+y2ddxx=0 x2ydydx+y21=02xydydx=-y2dydx=-y22xydydx=-y2xput x=1y2 from equation idydx=-y21y22dydx=-y32dydx+y3=0

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