`(1+x+xy^(2))(dy)/(dx)+(y+y^(3))=0`

(dy)/(dx)+(xy+y)/(xy+x)=0

x^(2)dy+(x^(2)-xy+y^(2))dx=0

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

(dy)/(dx)=(y^(2)-x)/(xy+y)

y^(2)dx+(x^(2)+xy+y^(2))dy=0

Solve (x^(3)-3xy^(2))dx+(3x^(2)y-y^(3))dy=0

xy^(2)((dy)/(dx))-2y^(3)=2x^(3) given y=1 at x=1

2xy + y^(2) - 2x^(2)(dy)/(dx) = 0, y = 2 when x = 1

2xy + y^(2) - 2x^(2)(dy)/(dx) = 0, y = 2 when x = 1