Find the general solution of the differential equations:`(x+3y^2)(dx)/(dy)=y(y >0)`

Explanation

`(x+3y^(2))(dy)/(dx)=yimpliesy(dx)/(dy)=x+3y^(2)`
`implies (dx)/(dy)-(1)/(y)x=3y`
Here, `P=-(1)/(y)`, `Q=3y`
`I,F.=e^(int-(1)/(y)dy)=e^(-logy)`
`=e^(log(y^(-1)))=y^(-1)=(1)/(y)`
and general solution :
`x((1)/(y))=int3y((1)/(y))dy+c`
`=int3dy+c=3y+c`
`implies x=3y^(2)+cy`