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The solution of differential equation x^...

The solution of differential equation `x^(2)(x dy + y dx) = (xy - 1)^(2) dx` is (where c is an arbitrary constant)

A

`xy-1=cx`

B

`xy-1=cx^(2)`

C

`(1)/(xy-1)=(1)/(x)+c`

D

`(1)/((xy-1)^(3))=(1)/(x^(3))+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^(2)(xdy+ydx)=(xy-1)^(2)dx rArr int (d(xy))/((xy-1)^(2))= int (dx)/(x^(2)) rArr (-1)/((xy-1))=(-1)/(x)+c`
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