Find the general solution of each of the following differential equations:
`(1-x^(2))dy +xy(1-y)dx =0`

Answer

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

Explanation

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