Find the general solution of each of the following differential equations:
`y(1-x^(2))(dy)/(dx)=x(1+y^(2))`

Answer

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

Explanation

`int (2y)/((1+y^(2)))dy= -int (-2x)/((1-x^(2)))dx rArr log|1+y^(2)|+log|1-x^(2)|=log|C_(1)|`
` rArr (1+y^(2))(1-x^(2))= pm C_(1)=C. `