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Solve (x-y^(2)x)dx=(y-x^(2)y)dy....

Solve `(x-y^(2)x)dx=(y-x^(2)y)dy`.

Text Solution

Verified by Experts

The correct Answer is:
`(x^(2)-1)=C(y^(2)-1)`
We have `x(1-y^(2))dx=y(1-x^(2))dy`
`therefore (2x)/(x^(2)-1)dx=(2y)/(y^(2)-1)dy`
Integrating both sides, we get
`log_(e)(x^(2)-1)=log_(e)(y^(2)-1)log_(e)C`
`therefore (x^(2)-1)=C(y^(2)-1)`
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