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

Answer

`(x^(2)-1)=C(y^(2)-1)`

Explanation

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)`