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

Answer

`y =1 +C_(1)xy`

Explanation

`int (1)/(y(y-1))dy = int (1)/(x)dx rArr int {(1)/((y-1))-(1)/(y)}dy=int (1)/(x) dx " " `[by partial fractions]
` rArr log|y-1| - log|y|=log|x|+log|C|`
`rArr (y-1)=pm C xy rArr (y-1)=C_(1)xy rArr y =1+C_(1)xy.`